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SPIRES-BOOKS: FIND KEYWORD COMMUTATIVE RINGS AND ALGEBRAS *END*INIT* use /tmp/qspiwww.webspi1/14945.11 QRY 131.225.70.96 . find keyword commutative rings and algebras ( in books using www Cover
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Call number:9783319508535:ONLINE Show nearby items on shelf
Title:Algebra II Textbook for Students of Mathematics
Author(s): Alexey L Gorodentsev
Date:2017
Size:1 online resource (XV, 370 p. 155 illus., 2 illus. in color p.)
Contents:§1Tensor Products -- §2 Tensor Algebras -- §3 Symmetric Functions -- §4 Calculus of Arrays, Tableaux, and Diagrams -- §5 Basic Notions of Representation Theory -- §6 Representations of Finite Groups in Greater Detail -- §7
Representations of Symmetric Groups -- §8 sl_2-Modules -- §9 Categories and Functors -- §10 Extensions of Commutative Rings -- §11 Affine Algebraic Geometry -- §12 Algebraic Manifolds -- §13 Algebraic Field Extensions -- §14 Examples
of Galois Groups -- References -- Hints to Some Exercises -- Index
ISBN:9783319508535
Series:eBooks
Series:Springer eBooks
Series:Springer 2017 package
Keywords: Mathematics , Algebra , Mathematics , Algebra
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Call number:SPRINGER-2016-9783319388557:ONLINE Show nearby items on shelf
Title:Multiplicative Ideal Theory and Factorization Theory Commutative and Non-commutative Perspectives
Author(s):
Date:2016
Size:1 online resource (407 p.)
Note:10.1007/978-3-319-38855-7
Contents:Multiplicative Ideal Theory in Non-commutative Rings (E. Akalan, H. Marubayashi) -- About number fields with Pólya group of order ≤ 2 (D. Adam, J.-L. Chabert) -- The interplay of Invariant Theory with Multiplicative Ideal Theory and with Arithmet ic Combinatorics (K. Cziczler, M. Domokos, A. Geroldinger) -- Ring and semigroup constructions (M. D'Anna) -- New Distinguished Classes of Spectral Spaces (C.A. Finocchiaro, M. Fontana, D. Spirito) -- Relative polynomial closure and monadically Krull mono ids of integer-valued polynomials (S. Frisch).-An overview of the computational aspects of nonunique factorization invariants (P.A. García-Sánchez).-Arithmetic of Mori domains and monoids: The global case (F. Kainrath) -- Prüfer Domains of Integer-Valu ed Polynomials (K.A. Loper, M. Syvuk) -- Lobal Properties of Integral Domains (T.G. Lucas) -- Topological aspects of irredundant intersections of ideals and valuation rings (B. Olberding) -- Noetherian semigroup algebras and beyond (J. Okniński)
-- Idempotent pairs and PRINC domains (G. Peruginelli, L. Salce, P. Zanardo) -- Some recent results and open problems on sets of lengths of Krull monoids with finite class group (W.A. Schmid) -- Factorizations of elements in noncommutative rings: A survey (D. Smertnig)
ISBN:9783319388557
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Springer Proceedings in Mathematics & Statistics: 170
Keywords: Mathematics , Algebraic geometry , Associative rings , Rings (Algebra) , Commutative algebra , Commutative rings , Group theory , Number theory , Mathematics , Commutative Rings and Algebras , Number Theory , Group Theory and Generalizations , Associative Rings and Algebras , Algebraic Geometry
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Call number:SPRINGER-2016-9783319267654:ONLINE Show nearby items on shelf
Title:On the Geometry of Some Special Projective Varieties
Author(s): Francesco Russo
Date:2016
Edition:1st ed. 2016
Size:1 online resource (232 p.)
Note:10.1007/978-3-319-26765-4
Contents:Preface.-Introduction -- 1.Tangent cones, tangent spaces, tangent stars secant, tangent and tangent star varieties to an algebraic variety -- 2.Basics of Deformation Theory of Rational Curves on Projective Varieties -- 3.Fulton-Hansen Connectedness Theorem, Scorza Lemma and their applications to projective geometry -- 4.Local quadratic entry locus manifolds and conic connected manifolds -- 5.Hartshorne Conjectures and Severi varieties -- 6.Varieties n-covered by curves of a fixed degree and the XJC -- 7. Hypersurfaces with vanishing hessian.-Bibliography
ISBN:9783319267654
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Lecture Notes of the Unione Matematica Italiana: 18
Keywords: Mathematics , Algebraic geometry , Commutative algebra , Commutative rings , Geometry , Mathematics , Algebraic Geometry , Commutative Rings and Algebras , Geometry
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Call number:SPRINGER-2016-9783319264370:ONLINE Show nearby items on shelf
Title:Minimal Free Resolutions over Complete Intersections
Author(s): David Eisenbud
Date:2016
Edition:1st ed. 2016
Size:1 online resource (107 p.)
Note:10.1007/978-3-319-26437-0
ISBN:9783319264370
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Lecture Notes in Mathematics: 2152
Keywords: Mathematics , Algebraic geometry , Category theory (Mathematics) , Homological algebra , Commutative algebra , Commutative rings , Physics , Mathematics , Commutative Rings and Algebras , Algebraic Geometry , Category Theory, Homological Algebra , Theoretical, Mathematical and Computational Physics
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Call number:SPRINGER-2012-9783034802604:ONLINE Show nearby items on shelf
Title:Representations of Finite Groups: Local Cohomology and Support [electronic resource]
Author(s): David J Benson
Srikanth Iyengar
Henning Krause
Date:2012
Publisher:Basel : Springer Basel
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The seminar focuses on a recent solution, by the authors, of a long standing problem concerning the stable module category (of not necessarily finite dimensional representations) of a finite group. The proof draws on ideas fromcommutative algebra, co homology of groups, and stable homotopy theory. The unifying theme is a notion of support which provides a geometric approach for studying various algebraic structures. The prototype for this has been DanielQuillens description of the algebraic variety co rresponding to the cohomology ring of a finite group, based on which Jon Carlson introduced support varieties for modular representations. This has made it possible to apply methods ofalgebraic geometry to obtain representation theoretic information. Thei r work has inspired the development of analogous theories in various contexts, notably modules over commutative complete intersection rings and over cocommutativeHopf algebras. One of the threads in this development has been the classification of thick or localizing subcategories of various triangulated categories of representations. This story started with Mike Hopkins classification ofthick subcategories of the perfect complexes over a commutative Noetherian ring, followed by a classification of localiz ing subcategories of its full derived category, due to Amnon Neeman. The authors have been developing an approachto address such classification problems, based on a construction of local cohomology functors and support for triangulated categories with rin g of operators. The book serves as an introduction to this circle of ideas
Note:Springer eBooks
Contents:Preface
1 Monday
1.1 Overview
1.2 Modules over group algebras
1.3 Triangulated categories
1.4 Exercises
2 Tuesday
2.1 Perfect complexes over commutative rings
2.2 Brown representability and localization
2.3 The stable module category of a finite group
2.4 Exercises
3 Wednesday
3.1
3.2 Koszul objects and support
3.3 The homotopy category of injectives
3.4 Exercises
4 Thursday
4.1 Stratifying triangulated categories
4.2 Consequences of stratification
4.3 The Klein four group
4.4 Exercises
5 Friday
5.1 Localising subcategories of D
ISBN:9783034802604
Series:e-books
Series:SpringerLink (Online service)
Series:Oberwolfach Seminars : v43
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Group theory
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Call number:SPRINGER-2012-9780817646424:ONLINE Show nearby items on shelf
Title:Sheaves of Algebras over Boolean Spaces [electronic resource]
Author(s): Arthur Knoebel
Date:2012
Publisher:Boston, MA : Birkhuser Boston : Imprint: Birkhuser
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Sheaves of Algebras over Boolean Spaces comprehensively covers sheaf theory as applied to universal algebra. Sheaves decompose general algebras into simpler pieces called the stalks. A classical case is commutative von Neumannregular rings, whose sta lks are fields. Other classical theorems also extend to shells, a common generalization of rings and lattices. This text presents intuitive ideas from topology such as the notion of metric space and the conceptof central idempotent from ring theory. These lead to the abstract notions of complex and factor element, respectively. Factor elements are defined by identities, discovered for shells for the first time, explaining why centralelements in rings and lattices have their particular form. Categorical fo rmulations of the many representations by sheaves begin with adjunctions and move to equivalences as the book progresses, generalizing Stones theorem forBoolean algebras. Half of the theorems provided in the text are new the rest are presented in a cohere nt framework, starting with the most general, and proceeding to specific applications. Many open problems and research areas areoutlined, including a final chapter summarizing applications of sheaves in diverse fields that were not covered earlier in the book. This monograph is suitable for graduate students and researchers, and it will serve as an excellentreference text for those who wish to learn about sheaves of algebras
Note:Springer eBooks
Contents:Preface
Introduction
Algebra
Tools
Complexes and their Sheaves
Boolean Subsemilattices
Sheaves from Factor Congruences
Shells
Baer
Stone Shells
Strict Shells
Varieties Generated by Preprimal Algebras
Return to General Algebras
Further Examples Pointing to Future Research
List of Symbols
References
Index
ISBN:9780817646424
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Topology
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Call number:SPRINGER-2011-9783642110368:ONLINE Show nearby items on shelf
Title:Some Aspects of Ring Theory [electronic resource]
Author(s): I. N Herstein
Date:2011
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:S. Amitsur: Associative rings with identities.- I.N. Herstein: Topics in ring theory.- N. Jacobson: Representation theory of Jordan algebras.- I. Kaplansky: The theory of homological dimension.- D. Buchsbaum: Complexes in localring theory.- P.H. Cohn : Two topics in ring theory.- A.W. Goldie: Non-commutative localisation
Note:Springer eBooks
Contents:S. Amitsur: Associative rings with identities
I.N. Herstein: Topics in ring theory
N. Jacobson: Representation theory of Jordan algebras
I. Kaplansky: The theory of homological dimension
D. Buchsbaum: Complexes in local ring theory
P.H. Cohn: Two topics in ring theory
A.W. Goldie: Non
commutative localisation
ISBN:9783642110368
Series:e-books
Series:SpringerLink (Online service)
Series:C.I.M.E. Summer Schools : v37
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Differential equations, partial
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Call number:SPRINGER-2011-9781441969903:ONLINE Show nearby items on shelf
Title:Commutative Algebra [electronic resource] : Noetherian and Non-Noetherian Perspectives
Author(s): Marco Fontana
Salah-Eddine Kabbaj
Bruce Olberding
Irena Swanson
Date:2011
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Commutative algebra is a rapidly growing subject that is developing in many different directions. This volume presents several of the most recent results from various areas related to both Noetherian and non-Noetherian commutativealgebra. This volume contains a collection of invited survey articles by some of the leading experts in the field. The authors of these chapters are internationally renowned for their important contributions to various aspects ofcurrent research in commutative algebra. Some topics presented in the volume include: generalizations of cyclic modules, zero divisor graphs, class semigroups, forcing algebras, syzygy bundles, tight closure, Gorenstein dimensions,tensor products of algebras over fields, as well as many others. This book is intended for researchers and graduate students interested in studying commutative algebra
Note:Springer eBooks
Contents:Introduction
1. Principal
like Ideals and Related Polynomial Content Conditions (D.D. Anderson)
2. Zero
divisor Graphs in Commutative Rings (D.F. Anderson, M. Axtell, J. Stickles)
3. Class Semigroups and T
class Semigroups of Domains (S. Bazzoni, S. Kabbaj)
4. Forcing Algebras, Syzygy Bundles, and Tight Closure (H. Brenner)
5. Beyond Totally Reflexive Modules and Back: A Survey on Gorenstein Dimensions (L.W. Christensen, H.B. Foxby, H. Holm)
6. On V
domains: A Survey (M. Fontana, M. Zafrullah)
7. Tensor Products of Algebras Over a Field (H. Haghighi, M. Tousi, S. Yassemi
ISBN:9781441969903
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Algebra
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Call number:SPRINGER-2009-9783764388584:ONLINE Show nearby items on shelf
Title:Selected Works of A.I. Shirshov [electronic resource]
Author(s): Leonid Bokut
Ivan Shestakov
Victor Latyshev
Efim Zelmanov
Date:2009
Publisher:Basel : Birkhuser Basel
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This book presents translations of selected works of the famous Russian mathematician A.I. Shirshov (19211981). He was a pioneer in several directions of associative, Lie, Jordan, and alternative algebras, as well as groupsand projective planes. His name is associated with notions and results on Grbner-Shirshov bases, the Composition-Diamond Lemma, the Shirshov-Witt Theorem, the Lazard-Shirshov elimination process, Shirshovs Height Theorem,Lyndon-Shirshov words, Hall-Shirshov bases, Shirshovs theorem on the Kurosh problem for alternative and Jordan algebras, and Shirshovs theorem on the speciality of Jordan algebras with two generators. Shirshovs ideas were usedby his student Efim Zelmanov for the solution of the Restricted Burnside Problem. Several famous algebraists provide in this book detailed comments on the impact of Shirshovs work on current algebra
Note:Springer eBooks
Contents:From the contents: Publications of A.I. Shirshov: Subalgebras of free Lie algebras
On the representation of Lie rings in associative rings
Subalgebras of free commutative and free anticommutative algebras
On special J
rings
Some theorems on embedding of rings
On some nonassociative nil
rings and algebraic algebras
On rings with identical relations
On free Lie rings
On a problem of Levitzki
Some problems in the theory of rings that are nearly associative
Some algorithmic problems for e
algebras
Some algorithmic problems for Lie algebras
On a hypothesis in the
ISBN:9783764388584
Series:e-books
Series:SpringerLink (Online service)
Series:Contemporary Mathematicians
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Mathematics_$xHistory
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Call number:SPRINGER-2009-9780387763569:ONLINE Show nearby items on shelf
Title:Polytopes, Rings, and K-Theory [electronic resource]
Author(s): Joseph Gubeladze
Winfried Bruns
Date:2009
Edition:1
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This book treats the interaction between discrete convex geometry, commutative ring theory, algebraic K-theory, and algebraic geometry. The basic mathematical objects are lattice polytopes, rational cones, affine monoids, thealgebras derived from the m, and toric varieties. The book discusses several properties and invariants of these objects, such as efficient generation, unimodular triangulations and covers, basic theory of monoid rings, isomorphismproblems and automorphism groups, homological prope rties and enumerative combinatorics. The last part is an extensive treatment of the K-theory of monoid rings, with extensions to toric varieties and their intersection theory. Thismonograph has been written with a view towards graduate students and resear chers who want to study the cross-connections of algebra and discrete convex geometry. While the text has been written from an algebraist's view point, alsospecialists in lattice polytopes and related objects will find an up-to-date discussion of affine m onoids and their combinatorial structure. Though the authors do not explicitly formulate algorithms, the book takes a constructiveapproach wherever possible. Winfried Bruns is Professor of Mathematics at Universitt Osnabrck. Joseph Gubeladze is Professor of Mathematics at San Francisco State University
Note:Springer eBooks
Contents:Preface
Polytopes, cones, and complexes
Affine monoids and their Hilbert bases
Multiples of lattice polytopes
Monoid algebras
Isomorphisms and automorphisms
Homological properties and Hilbert functions
Grbner bases, triangulations, and Koszul algebras
Projective modules over monoid rings
Bass
Whitehead groups of monoid rings
Varieties
References
Notation
Index
ISBN:9780387763569
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Monographs in Mathematics, 1439-7382
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , K-theory , Discrete groups
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Call number:SPRINGER-2008-9783764386061:ONLINE Show nearby items on shelf
Title:Quadratic Mappings and Clifford Algebras [electronic resource]
Author(s): Jacques Helmstetter
Artibano Micali
Date:2008
Publisher:Basel : Birkhuser Basel
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:After a classical presentation of quadratic mappings and Clifford algebras over arbitrary rings (commutative, associative, with unit), other topics involve more original methods: interior multiplications allow an effectivetreatment of deformations of Clifford algebras the relations between automorphisms of quadratic forms and Clifford algebras are based on the concept of the Lipschitz monoid, from which several groups are derived and theCartan-Chevalley theory of hyperbolic spaces becomes much more g eneral, precise and effective
Note:Springer eBooks
Contents:Algebraic Preliminaries
Quadratic Mappings
Clifford Algebras
Comultiplications. Exponentials. Deformations
Orthogonal Groups and Lipschitz Groups
Further Algebraic Developments
Hyperbolic Spaces
Complements about Witt Rings and Other Topics
ISBN:9783764386061
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra
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Call number:SPRINGER-2007-9780387715681:ONLINE Show nearby items on shelf
Title:Abstract Algebra [electronic resource]
Author(s): Pierre Antoine Grillet
Date:2007
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Abstract Algebra is a clearly written, self-contained basic algebra text for graduate students, with a generous amount of additional material that suggests the scope of contemporary algebra. The first chapters blend standardcontents with a careful in troduction to proofs with arrows. The last chapters, on universal algebras and categories, including tripleability, give valuable general views of algebra. There are over 1400 exercises, at varying degrees ofdifficulty. For the new edition, the author has completely rewritten the entire text, streamlining the first chapters for rapid access to Galois theory, removing some material, and adding introductions to Groebner bases, Ext and Tor,and other topics. From a review of the First Edition: ...combines an exceptionally accessible discussion of the basic material with a just as thorough and well-organized treatment of the many additional (advanced) topics included....represents an outstanding introduction to modern abstract algebra as a whole, with many uni que features. It captivates the reader by its remarkable diversity, comprehensiveness, elegant succinctness, and coherence. - Werner Kleinert,Zentralblatt
Note:Springer eBooks
Contents:Groups
Structure of Groups
Rings
Field Extensions
Galois Theory
Fields with Orders or Valuations
Commutative Rings
Modules
Semisimple Rings and Modules
Projectives and Injectives
Constructions
Ext and Tor
Algebras
Lattices
Universal Algebra
Categories
ISBN:9780387715681
Series:e-books
Series:SpringerLink (Online service)
Series:Graduate Texts in Mathematics, 0072-5285 : v242
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Group theory
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Call number:SPRINGER-2006-9783540295235:ONLINE Show nearby items on shelf
Title:Algebraic Theory of Locally Nilpotent Derivations [electronic resource]
Author(s): Gene Freudenburg
Date:2006
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This book explores the theory and application of locally nilpotent derivations, which is a subject of growing interest and importance not only among those in commutative algebra and algebraic geometry, but also in fields such asLie algebras and diffe rential equations. The author provides a unified treatment of the subject, beginning with 16 First Principles on which the entire theory is based. These are used to establish classical results, such asRentschlers Theorem for the plane, right up to the mos t recent results, such as Makar-Limanovs Theorem for locally nilpotent derivations of polynomial rings. Topics of special interest include: progress in the dimension threecase, finiteness questions (Hilberts 14th Problem), algorithms, the Makar-Limanov in variant, and connections to the Cancellation Problem and the Embedding Problem. The reader will also find a wealth of pertinent examples and openproblems and an up-to-date resource for research
Note:Springer eBooks
Contents:0 Introduction
1 First Principles
2 Further Properties of Locally Nilpotent Derivations
3 Polynomial Rings
4 Dimension Two
5 Dimension Three
6 Linear Actions of Vector Groups
7 Non
Finitely Generated Kernels
8 Algorithms
9 The Makar
Limanov and Derksen Invariants
10 Slices, Embeddings and Cancellation
11 Epilogue
References
Index
ISBN:9783540295235
Series:e-books
Series:SpringerLink (Online service)
Series:Encyclopaedia of Mathematical Sciences, Invariant Theory and Algebraic Transformation Groups VII, 0938-0396 : v136
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Algebra , Topological Groups
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Call number:SPRINGER-2006-9780387367170:ONLINE Show nearby items on shelf
Title:Multiplicative Ideal Theory in Commutative Algebra [electronic resource] : A Tribute to the Work of Robert Gilmer
Author(s): James W Brewer
Sarah Glaz
William J Heinzer
Bruce M Olberding
Date:2006
Publisher:Boston, MA : Springer US
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:For over forty years, Robert Gilmers numerous articles and books have had a tremendous impact on research in commutative algebra. It is not an exaggeration to say that most articles published today in non-Noetherian ringtheory, and some in Noetherian ring theory as well, originated in a topic that Gilmer either initiated or enriched by his work. This volume, a tribute to his work, consists of twenty-four articles authored by Robert Gilmers mostprominent students and followers. These articles combine surveys of past work by Gilmer and others, recent results which have never before seen print, open problems, and extensive bibliographies. In a concluding article, Robert Gilmerpoints out directions for future research, highlighting the open problems in t he areas he considers of importance. Robert Gilmers article is followed by the complete list of his published works, his mathematical genealogical tree,information on the writing of his four books, and reminiscences about Robert Gilmers contributions to t he stimulating research environment in commutative algebra at Florida State in the middle 1960s. The entire collection providesan in-depth overview of the topics of research in a significant and large area of commutative algebra. Audience This book is int ended for researchers and graduate students in the field of commutative algebra
Note:Springer eBooks
Contents:Commutative rngs
Robert Gilmers work on semigroup rings
Numerical semigroup algebras
Prfer rings
Subrings of zero
dimensional rings
Old problems and new questions around integer
valued polynomials and factorial sequences
Robert Gilmers contributions to the theory of integer
valued polynomials
Progress on the dimension question for power series rings
Some research on chains of prime ideals influenced by the writings of Robert Gilmer
Direct
sum decompositions over one
dimensional Cohen
Macaulay local rings
An historical overview of Kronecker function rings,
ISBN:9780387367170
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Group theory
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Call number:SPRINGER-2005-9783540274278:ONLINE Show nearby items on shelf
Title:Lie Algebras and Algebraic Groups [electronic resource]
Author(s): Patrice Tauvel
Rupert W. T Yu
Date:2005
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The theory of Lie algebras and algebraic groups has been an area of active research in the last 50 years. It intervenes in many different areas of mathematics: for example invariant theory, Poisson geometry, harmonic analysis,mathematical physics. Th e aim of this book is to assemble in a single volume the algebraic aspects of the theory so as to present the foundation of the theory in characteristic zero. Detailed proofs are included and some recent resultsare discussed in the last chapters. All the prerequisites on commutative algebra and algebraic geometry are included
Note:Springer eBooks
Contents:Preface
Results on topological spaces
Rings and modules
Integral extensions
Factorial rings
Field extensions
Finitely generated algebras
Gradings and filtrations
Inductive limits
Sheaves of functions
Jordan decomposition and some basic results on groups
Algebraic sets
Prevarieties and varieties
Projective varieties
Dimension
Morphisms and dimension
Tangent spaces
Normal varieties
Root systems
Lie algebras
Semisimple and reductive Lie algebras
Algebraic groups
Affine algebraic groups
Lie algebra of an algebraic group
Corres
ISBN:9783540274278
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Monographs in Mathematics, 1439-7382
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Geometry, algebraic , Group theory , Topological Groups
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Call number:SPRINGER-2005-9783540264743:ONLINE Show nearby items on shelf
Title:Basic Notions of Algebra [electronic resource]
Author(s): Igor R Shafarevich
Date:2005
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:From the reviews: This is one of the few mathematical books, the reviewer has read from cover to cover ... The main merit is that nearly on every page you will find some unexpected insights... Zentralblatt fr Mathematik undIhre Grenzgebiete, 1991 ... which I read like a novel and undoubtedly will become a classic. ... A merit of the book under review is that it contains several important articles from journals which are not all so easily accessible. ...Furthermore, at the end of the book, there are so me Notes by the author which are indispensible for the necessary historical background information. ... This valuable book should be on the shelf of every algebraist and algebraicgeometer. Nieuw Archief voor Wiskunde, 1992 ... There are few proofs in full , but there is an exhilarating combination of sureness of foot and lightness of touch in the exposition ... which transports the reader effortlessly acrossthe whole spectrum of algebra.... The challenge to Ezekiel, Can these bones live? is, all too often, the reaction of students when introduced to the bare bones of the concepts and constructs of modern algebra. Shafarevich's book -which reads as comfortably as an extended essay - breathes life into the skeleton and will be of interest to many classes of readers... The Mathematical Gazette, 1991 ... According to the preface, the book is addressed tostudents of mathematics in the first years of an undergraduate course, or theoretical physicists or mathematicians from outside algebra wanting to get an impre ssion of the spirit of algebra and its place in mathematics. I thinkthat this promise is fully justified. The beginner, the experts and also the interested scientist who had contact with algebraic notions - all will read this exceptional book with great p leasure and benefit. Zeitschrift frKristallographie, 1991
Note:Springer eBooks
Contents:Preface
1 What is Algebra?
2 Fields
3 Commutative Rings
4 Homomorphisms and Ideals
5 Modules
6 Algebraic Aspects of Dimension
7 The Algebraic View of Infinitesimal Notions
8 Noncommutative Rings
9 Modules and Noncommutative Rings
10 Semisimple Modules and Rings
11 Division Algebras of Finite Rank
12 The Notion of a Group
13 Examples of Groups: Finite Groups
14 Examples of Groups: Infinite Discrete Groups
15 Examples of Groups : Lie Groups and Algebraic Groups
16 General Results of Group Theory
17 Group Representations
18 Some Applications of
ISBN:9783540264743
Series:e-books
Series:SpringerLink (Online service)
Series:Encyclopaedia of Mathematical Sciences, 0938-0396 : v11
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , K-theory , Topological Groups
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Call number:SPRINGER-2005-9780817644437:ONLINE Show nearby items on shelf
Title:Introduction to Plane Algebraic Curves [electronic resource]
Author(s): Ernst Kunz
Date:2005
Publisher:Boston, MA : Birkhuser Boston
Size:1 online resource
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Note:This work treats an introduction to commutative ring theory and algebraic plane curves, requiring of the student only a basic knowledge of algebra, with all of the algebraic facts collected into several appendices that can beeasily referred to, as ne eded. Kunz's proven conception of teaching topics in commutative algebra together with their applications to algebraic geometry makes this book significantly different from others on plane algebraic curves. Theexposition focuses on the purely algebraic as pects of plane curve theory, leaving the topological and analytical viewpoints in the background, with only casual references to these subjects and suggestions for further reading. Mostimportant to this text: * Emphasizes and utilizes the theory of filter ed algebras, their graduated rings and Rees algebras, to deduce basic facts about the intersection theory of plane curves * Presents residue theory in the affineplane and its applications to intersection theory * Methods of proof for the RiemannRoch theor em conform to the presentation of curve theory, formulated in the language of filtrations and associated graded rings * Examples,exercises, figures and suggestions for further study round out this fairly self-contained textbook From a review of the German edition: [T]he reader is invited to learn some topics from commutative ring theory by mainly studyingtheir illustrations and applications in plane curve theory. This methodical approach is certainly very enlightening and efficient for both teachers and s tudents The whole text is a real masterpiece of clarity, rigor, comprehension,methodical skill, algebraic and geometric motivationhighly enlightening, motivating and entertaining at the same time One simply cannot do better in writing such a textbook. Zen tralblatt MATH
Note:Springer eBooks
Contents:Preface
Conventions and Notation
Part I: Plane Algebraic Curves Affine Algebraic Curves Projective Algebraic Curves The Coordinate Ring of an Algebraic Curve and the Intersections of Two Curves Rational Functions on Algebraic Curves IntersectionMultiplicity and Intersection C ycle of Two Curves Regular and Singular Points of Algebraic Curves. Tangents More on Intersection Theory. Applications Rational Maps. Parametric Representations of Curves Polars and Hessians ofAlgebraic Curves Elliptic Curves Residue Calculus Applications of Residue Theory to Curves The Riemann
Roch Th
ISBN:9780817644437
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Algebra , Field theory (Physics) , Algebraic topology
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Call number:SPRINGER-2005-9780387271033:ONLINE Show nearby items on shelf
Title:Combinatorial Commutative Algebra [electronic resource]
Author(s): Ezra Miller
Bernd Sturmfels
Date:2005
Publisher:New York, NY : Springer New York
Size:1 online resource
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Note:Combinatorial commutative algebra is an active area of research with thriving connections to other fields of pure and applied mathematics. This book provides a self-contained introduction to the subject, with an emphasis oncombinatorial techniques fo r multigraded polynomial rings, semigroup algebras, and determinantal rings. The eighteen chapters cover a broad spectrum of topics, ranging from homological invariants of monomial ideals and their polyhedralresolutions, to hands-on tools for studying alg ebraic varieties with group actions, such as toric varieties, flag varieties, quiver loci, and Hilbert schemes. Over 100 figures, 250 exercises, and pointers to the literature make thisbook appealing to both graduate students and researchers. Ezra Miller received his doctorate in 2000 from UC Berkeley. After two years at MIT in Cambridge and one year at MSRI in Berkeley, he is currently Assistant Professor at theUniversity of Minnesota, Twin Cities. Miller was awarded an Alfred P. Sloan Dissertation Fello wship in 1999 and an NSF Postdoctoral Fellowship in 2000. Besides his mathematical interests, which include combinatorics, algebraicgeometry, homological algebra, and polyhedral geometry, Miller is fond of music theory and composition, molecular biology, and ultimate frisbee. Bernd Sturmfels received doctoral degrees in 1987 from the University of Washington,Seattle and TU Darmstadt, Germany. After two postdoc years at the IMA in Minneapolis and RISC-Linz in Austria, he taught at Cornell University before joining UC Berkeley in 1995, where he is now Professor of Mathematics and ComputerScience. A leading experimentalist among mathematicians, Sturmfels has authored seven books and over 130 research articles in the areas of combinatorics, algebraic geometry , symbolic computation, and their applications, and he hasmentored 16 doctoral students
Note:Springer eBooks
Contents:Monomial Ideals
Squarefree monomial ideals
Borel
fixed monomial ideals
Three
dimensional staircases
Cellular resolutions
Alexander duality
Generic monomial ideals
Toric Algebra
Semigroup rings
Multigraded polynomial rings
Syzygies of lattice ideals
Toric varieties
Irreducible and injective resolutions
Ehrhart polynomials
Local cohomology
Determinants
Plcker coordinates
Matrix Schubert varieties
Antidiagonal initial ideals
Minors in matrix products
Hilbert schemes of points
ISBN:9780387271033
Series:e-books
Series:SpringerLink (Online service)
Series:Graduate Texts in Mathematics, 0072-5285 : v227
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Algebra , Combinatorics
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Call number:SPRINGER-2004-9783540446460:ONLINE Show nearby items on shelf
Title:The Valuative Tree
Author(s): Charles Favre
Date:2004
Size:1 online resource (244 p.)
Note:10.1007/b100262
Contents:1 Generalities -- 1.1 Setup -- 1.2 Valuations -- 1.3 Krull Valuations -- 1.4 Plane Curves -- 1.5 Examples of Valuations -- 1.6 Valuations Versus Krull Valuations -- 1.7 Sequences of Blowups and Krull Valuations -- 2 MacLane’s Method
-- 2.1 Sequences of Key Polynomials -- 2.2 Classification -- 2.3 Graded Rings and Numerical Invariants -- 2.4 From Valuations to SKP’s -- 2.5 A Computation -- 3 Tree Structures -- 3.1 Trees -- 3.2 Nonmetric Tree Structure on V -- 3.3
Parameterization of V by Skewness -- 3.4 Multiplicities -- 3.5 Approximating Sequences -- 3.6 Thinness -- 3.7 Value Semigroups and Approximating Sequences -- 3.8 Balls of Curves -- 3.9 The Relative Tree Structure -- 4 Valuations
Through Puiseux Series -- 4.1 Puiseux Series and Valuations -- 4.2 Tree Structure -- 4.3 Galois Action -- 4.4 A Tale of Two Trees -- 4.5 The Berkovich Projective Line -- 4.6 The Bruhat-Tits Metric -- 4.7 Dictionary -- 5 Topologies --
5.1 The Weak Topology -- 5.2 The Strong Topology on V -- 5.3 The Strong Topology on Vqm -- 5.4 Thin Topologies -- 5.5 The Zariski Topology -- 5.6 The Hausdorff-Zariski Topology -- 5.7 Comparison of Topologies -- 6 The Universal Dual
Graph -- 6.1 Nonmetric Tree Structure -- 6.2 Infinitely Near Points -- 6.3 Parameterization and Multiplicity -- 6.4 The Isomorphism -- 6.5 Proof of the Isomorphism -- 6.6 Applications -- 6.7 The Dual Graph of the Minimal
Desingularization -- 6.8 The Relative Tree Structure -- 7 Tree Measures -- 7.1 Outline -- 7.2 More on the Weak Topology -- 7.3 Borel Measures -- 7.4 Functions of Bounded Variation -- 7.5 Representation Theorem I -- 7.6 Complex Tree
Potentials -- 7.7 Representation Theorem II -- 7.8 Atomic Measures -- 7.9 Positive Tree Potentials -- 7.10 Weak Topologies and Compactness -- 7.11 Restrictions to Subtrees -- 7.12 Inner Products -- 8 Applications of the Tree Analysis
-- 8.1 Zariski’s Theory of Complete Ideals -- 8.2 The Voûte étoilée -- A Infinitely Singular Valuations -- A.1 Characterizations -- A.2 Constructions -- B The Tangent Space at a Divisorial Valuation -- C Classification -- D
Combinatorics of Plane Curve Singularities -- D.1 Zariski’s Terminology for Plane Curve Singularities -- D.2 The Eggers Tree -- E.1 Completeness -- E.2 The Residue Field -- References
ISBN:9783540446460
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Lecture Notes in Mathematics: 1853
Keywords: Mathematics , Algebraic geometry , Commutative algebra , Commutative rings , Topology , Discrete mathematics , Mathematics , Discrete Mathematics , Algebraic Geometry , Commutative Rings and Algebras , Topology
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Call number:SPRINGER-2004-9781402020292:ONLINE Show nearby items on shelf
Title:Resolution of Curve and Surface Singularities in Characteristic Zero
Author(s): K Kiyek
Date:2004
Size:1 online resource (486 p.)
Note:10.1007/978-1-4020-2029-2
Contents:I Valuation Theory -- 1 Marot Rings -- 2 Manis Valuation Rings -- 3 Valuation Rings and Valuations -- 4 The Approximation Theorem For Independent Valuations -- 5 Extensions of Valuations -- 6 Extending Valuations to Algebraic
Overfields -- 7 Extensions of Discrete Valuations -- 8 Ramification Theory of Valuations -- 9 Extending Valuations to Non-Algebraic Overfields -- 10 Valuations of Algebraic Function Fields -- 11 Valuations Dominating a Local Domain --
II One-Dimensional Semilocal Cohen-Macaulay Rings -- 1 Transversal Elements -- 2 Integral Closure of One-Dimensional Semilocal Cohen-Macaulay Rings -- 3 One-Dimensional Analytically Unramified and Analytically Irreducible CM-Rings -- 4
Blowing up Ideals -- 5 Infinitely Near Rings -- III Differential Modules and Ramification -- 1 Introduction -- 2 Norms and Traces -- 3 Formally Unramified and Unramified Extensions -- 4 Unramified Extensions and Discriminants -- 5
Ramification For Quasilocal Rings -- 6 Integral Closure and Completion -- IV Formal and Convergent Power Series Rings -- 1 Formal Power Series Rings -- 2 Convergent Power Series Rings -- 3 Weierstraß Preparation Theorem -- 4 The
Category of Formal and Analytic Algebras -- 5 Extensions of Formal and Analytic Algebras -- V Quasiordinary Singularities -- 1 Fractionary Power Series -- 2 The Jung-Abhyankar Theorem: Formal Case -- 3 The Jung-Abhyankar Theorem:
Analytic Case -- 4 Quasiordinary Power Series -- 5 A Generalized Newton Algorithm -- 6 Strictly Generated Semigroups -- VI The Singularity Zq = XYp -- 1 Hirzebruch-Jung Singularities -- 2 Semigroups and Semigroup Rings -- 3 Continued
Fractions -- 4 Two-Dimensional Cones -- 5 Resolution of Singularities -- VII Two-Dimensional Regular Local Rings -- 1 Ideal Transform -- 2 Quadratic Transforms and Ideal Transforms -- 3 Complete Ideals -- 4 Factorization of Complete
Ideals -- 5 The Predecessors of a Simple Ideal -- 6 The Quadratic Sequence -- 7 Proximity -- 8 Resolution of Embedded Curves -- VIII Resolution of Singularities -- 1 Blowing up Curve Singularities -- 2 Resolution of Surface
Singularities I: Jung’s Method -- 3 Quadratic Dilatations -- 4 Quadratic Dilatations of Two-Dimensional Regular Local Rings -- 5 Valuations of Algebraic Function Fields in Two Variables -- 6 Uniformization -- 7 Resolution of Surface
Singularities II: Blowing up and Normalizing -- Appendices -- A Results from Classical Algebraic Geometry -- 1 Generalities -- 1.1 Ideals and Varieties -- 1.2 Rational Functions and Maps -- 1.3 Coordinate Ring and Local Rings -- 1.4
Dominant Morphisms and Closed Embeddings -- 1.5 Elementary Open Sets -- 1.6 Varieties as Topological Spaces -- 1.7 Local Ring on a Subvariety -- 2 Affine and Finite Morphisms -- 3 Products -- 4 Proper Morphisms -- 4.1 Space of
Irreducible Closed Subsets -- 4.3 Proper Morphisms -- 5 Algebraic Cones and Projective Varieties -- 6 Regular and Singular Points -- 7 Normalization of a Variety -- 8 Desingularization of a Variety -- 9 Dimension of Fibres -- 10
Quasifinite Morphisms and Ramification -- 10.1 Quasifinite Morphisms -- 10.2 Ramification -- 11 Divisors -- 12 Some Results on Projections -- 13 Blowing up -- 14 Blowing up: The Local Rings -- B Miscellaneous Results -- 1 Ordered
Abelian Groups -- 1.1 Isolated Subgroups -- 1.2 Initial Index -- 1.3 Archimedean Ordered Groups -- 1.4 The Rational Rank of an Abelian Group -- 2 Localization -- 3 Integral Extensions -- 4 Some Results on Graded Rings and Modules --
4.1 Generalities -- 4.3 Homogeneous Localization -- 4.4 Integral Closure of Graded Rings -- 5 Properties of the Rees Ring -- 6 Integral Closure of Ideals -- 6.1 Generalities -- 6.2 Integral Closure of Ideals -- 6.3 Integral Closure of
Ideals and Valuation Theory -- 7 Decomposition Group and Inertia Group -- 8 Decomposable Rings -- 9 The Dimension Formula -- 10 Miscellaneous Results -- 10.1 The Chinese Remainder Theorem -- 10.2 Separable Noether Normalization -- 10.3
The Segre Ideal -- 10.4 Adjoining an Indeterminate -- 10.5 Divisor Group and Class Group -- 10.6 Calculating a Multiplicity -- 10.7 A Length Formula -- 10.8 Quasifinite Modules -- 10.9 Maximal Primary Ideals -- 10.10 Primary
Decomposition in Non-Noetherian Rings -- 10.11 Discriminant of a Polynomial -- Index of Symbols
ISBN:9781402020292
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Algebras and Applications: 4
Keywords: Mathematics , Algebraic geometry , Commutative algebra , Commutative rings , Algebra , Field theory (Physics) , Functions of complex variables , Mathematics , Algebraic Geometry , Commutative Rings and Algebras , Field Theory and Polynomials , Several Complex Variables and Analytic Spaces
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Call number:SPRINGER-2003-9789401703451:ONLINE Show nearby items on shelf
Title:Endomorphism Rings of Abelian Groups
Author(s): Piotr A Krylov
Date:2003
Size:1 online resource (443 p.)
Note:10.1007/978-94-017-0345-1
Contents:I. General Results on Endomorphism Rings -- II. Groups as Modules over Their Endomorphism Rings -- III. Ring Properties of Endomorphism Rings -- IV. The Jacobson Radical of the Endomorphism Ring -- V. Isomorphism and Realization
Theorems -- VI. Hereditary Endomorphism Rings -- VII. Fully Transitive Groups -- References
ISBN:9789401703451
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Algebras and Applications: 2
Keywords: Mathematics , Associative rings , Rings (Algebra) , Commutative algebra , Commutative rings , Group theory , Mathematics , Associative Rings and Algebras , Group Theory and Generalizations , Commutative Rings and Algebras
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Call number:SPRINGER-2003-9789401703376:ONLINE Show nearby items on shelf
Title:Proceedings of the Third International Algebra Conference June 16–July 1, 2002 Chang Jung Christian University, Tainan, Taiwan
Author(s): Yuen Fong
Date:2003
Size:1 online resource (268 p.)
Note:10.1007/978-94-017-0337-6
ISBN:9789401703376
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Associative rings , Rings (Algebra) , Commutative algebra , Commutative rings , Algebra , Field theory (Physics) , Group theory , Nonassociative rings , Mathematics , Field Theory and Polynomials , Commutative Rings and Algebras , Associative Rings and Algebras , Non-associative Rings and Algebras , Group Theory and Generalizations
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Call number:SPRINGER-2003-9789401702157:ONLINE Show nearby items on shelf
Title:Cohomology Rings of Finite Groups With an Appendix: Calculations of Cohomology Rings of Groups of Order Dividing 64
Author(s): Jon F Carlson
Date:2003
Size:1 online resource (776 p.)
Note:10.1007/978-94-017-0215-7
Contents:1. Homological Algebra -- 2. Group Algebras -- 3. Projective Resolutions -- 4. Cohomology Products -- 5. Spectral Sequences -- 6. Norms and the Cohomology of Wreath Products -- 7. Steenrod Operations -- 8. Varieties and Elementary
Abelian Subgroups -- 9. Cohomology Rings of Modules -- 10. Complexity and Multiple Complexes -- 11. Duality Complexes -- 12. Transfers, Depth and Detection -- 13. Subgroup Complexes -- 14. Computer Calculations and Completion Tests --
Appendices: Calculations of the Cohomology Rings of Groups of Order Dividing 64 -- A— Notation and References -- B— Groups of Order 8 -- C— Groups of Order 16 -- D— Groups of Order 32 -- E— Groups of Order 64 -- F— Tables of Krull
Dimension and Depth -- G— Tables of Hilbert / Poincaré Series -- References
ISBN:9789401702157
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Algebras and Applications: 3
Keywords: Mathematics , Numerical analysis , Algebra , Category theory (Mathematics) , Homological algebra , Commutative algebra , Commutative rings , Geometry , Algebraic topology , Mathematics , Geometry , Category Theory, Homological Algebra , Algebra , Commutative Rings and Algebras , Numeric Computing , Algebraic Topology
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Call number:SPRINGER-2003-9783642557507:ONLINE Show nearby items on shelf
Title:Galois Theory of Linear Differential Equations
Author(s): Marius van der Put
Date:2003
Size:1 online resource (438 p.)
Note:10.1007/978-3-642-55750-7
Contents:Algebraic Theory -- 1 Picard-Vessiot Theory -- 2 Differential Operators and Differential Modules -- 3 Formal Local Theory -- 4 Algorithmic Considerations -- Analytic Theory -- 5 Monodromy, the Riemann-Hilbert Problem, and the
Differential Galois Group -- 6 Differential Equations on the Complex Sphere and the Riemann-Hilbert Problem -- 7 Exact Asymptotics -- 8 Stokes Phenomenon and Differential Galois Groups -- 9 Stokes Matrices and Meromorphic
Classification -- 10 Universal Picard-Vessiot Rings and Galois Groups -- 11 Inverse Problems -- 12 Moduli for Singular Differential Equations -- 13 Positive Characteristic -- Appendices -- A Algebraic Geometry -- A.1 Affine Varieties
-- A. 1.1 Basic Definitions and Results -- A. 1.2 Products of Affine Varieties over k -- A. 1.3 Dimension of an Affine Variety -- A. 1.4 Tangent Spaces, Smooth Points, and Singular Points -- A.2 Linear Algebraic Groups -- A.2.1 Basic
Definitions and Results -- A.2.2 The Lie Algebra of a Linear Algebraic Group -- A.2.3 Torsors -- B Tannakian Categories -- B.1 Galois Categories -- B.2 Affine Group Schemes -- B.3 Tannakian Categories -- C Sheaves and Cohomology -- C.l
Sheaves: Definition and Examples -- C.1.1 Germs and Stalks -- C.1.2 Sheaves of Groups and Rings -- C. 1.3 From Presheaf to Sheaf -- C. 1.4 Moving Sheaves -- C.l.5 Complexes and Exact Sequences -- C.2 Cohomology of Sheaves -- C.2.1 The
Idea and the Formahsm -- C.2.2 Construction of the Cohomology Groups -- C.2.3 More Results and Examples -- D Partial Differential Equations -- D. 1 The Ring of Partial Differential Operators -- D.2 Picard-Vessiot Theory and Some
Remarks -- List of Notation
ISBN:9783642557507
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics: 328
Keywords: Mathematics , Algebraic geometry , Commutative algebra , Commutative rings , Mathematical analysis , Analysis (Mathematics) , Differential equations , Number theory , Mathematics , Analysis , Number Theory , Commutative Rings and Algebras , Algebraic Geometry , Ordinary Differential Equations
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Call number:SPRINGER-2003-9783540450962:ONLINE Show nearby items on shelf
Title:Almost Ring Theory
Author(s):
Date:2003
Size:1 online resource (318 p.)
Note:10.1007/b10047
Contents:Introduction -- Homological Theory -- Almost Ring Theory -- Fine Study of Almost Projective Modules -- Henselian Pairs -- Valuation Theory -- Analytic Geometry -- Appendix -- References -- Index
ISBN:9783540450962
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Lecture Notes in Mathematics: 1800
Keywords: Mathematics , Algebra , Algebraic geometry , Category theory (Mathematics) , Homological algebra , Commutative algebra , Commutative rings , Field theory (Physics) , Mathematics , Algebra , Commutative Rings and Algebras , Algebraic Geometry , Category Theory, Homological Algebra , Field Theory and Polynomials
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Call number:SPRINGER-2003-9783540396802:ONLINE Show nearby items on shelf
Title:Gröbner Bases and the Computation of Group Cohomology
Author(s):
Date:2003
Size:1 online resource (144 p.)
Note:10.1007/b93836
Contents:Introduction -- Part I Constructing minimal resolutions: Bases for finite-dimensional algebras and modules The Buchberger Algorithm for modules Constructing minimal resolutions -- Part II Cohomology ring structure: Gröbner bases for
graded commutative algebras The visible ring structure The completeness of the presentation -- Part III Experimental results: Experimental results -- A. Sample cohomology calculations -- Epilogue -- References -- Index
ISBN:9783540396802
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Lecture Notes in Mathematics: 1828
Keywords: Mathematics , Associative rings , Rings (Algebra) , Group theory , Mathematics , Group Theory and Generalizations , Associative Rings and Algebras
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Call number:SPRINGER-2003-9783540396659:ONLINE Show nearby items on shelf
Title:C∞-Differentiable Spaces
Author(s): Juan A Navarro González
Date:2003
Size:1 online resource (196 p.)
Note:10.1007/b13465
Contents:Introduction -- 1. Differentiable Manifolds -- 2. Differentiable Algebras -- 3. Differentiable Spaces -- 4. Topology of Differentiable Spaces -- 5. Embeddings -- 6. Topological Tensor Products -- 7. Fibred Products -- 8. Topological
Localization -- 9. Finite Morphisms -- 10. Smooth Morphisms -- 11. Quotients by Compact Lie Groups -- A. Sheaves of Fréchet Modules -- B. Space of Jets -- References -- Index
ISBN:9783540396659
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Lecture Notes in Mathematics: 1824
Keywords: Mathematics , Commutative algebra , Commutative rings , Global analysis (Mathematics) , Manifolds (Mathematics) , Mathematics , Global Analysis and Analysis on Manifolds , Commutative Rings and Algebras
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Call number:SPRINGER-2003-9780857294289:ONLINE Show nearby items on shelf
Title:Basic Algebra Groups, Rings and Fields
Author(s): P. M Cohn
Date:2003
Size:1 online resource (465 p.)
Note:10.1007/978-0-85729-428-9
Contents:1. Sets -- 2. Groups -- 3. Lattices and Categories -- 4. Rings and Modules -- 5. Algebras -- 6. Multilinear Algebra -- 7. Field Theory -- 8. Quadratic Forms and Ordered Fields -- 9. Valuation Theory -- 10. Commutative Rings -- 11.
Infinite Field Extensions -- List of Notations -- Author Index
ISBN:9780857294289
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Algebra , Group theory , Mathematics , Algebra , Group Theory and Generalizations
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Call number:SPRINGER-2003-9780387217710:ONLINE Show nearby items on shelf
Title:Exercises in Classical Ring Theory
Author(s): T. Y Lam
Date:2003
Edition:Second Edition
Size:1 online resource (364 p.)
Note:10.1007/b97448
Contents:Wedderburn-Artin Theory -- Jacobson Radical Theory -- to Representation Theory -- Prime and Primitive Rings -- to Division Rings -- Ordered Structures in Rings -- Local Rings, Semilocal Rings, and Idempotents -- Perfect and
Semiperfect Rings
ISBN:9780387217710
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Associative rings , Rings (Algebra) , Commutative algebra , Commutative rings , Mathematics , Commutative Rings and Algebras , Associative Rings and Algebras
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Call number:SPRINGER-2002-9789401732673:ONLINE Show nearby items on shelf
Title:The Concise Handbook of Algebra
Author(s): Alexander V Mikhalev
Date:2002
Size:1 online resource (618 p.)
Note:10.1007/978-94-017-3267-3
Contents:A Semigroups -- B Groups -- C Rings, Modules, Algebras -- D Fields -- E Representation Theory -- F Lattices -- G Universal Algebra -- H Homological Algebra -- I Miscellaneous -- About the Authors
ISBN:9789401732673
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Algebra , Associative rings , Rings (Algebra) , Commutative algebra , Commutative rings , Field theory (Physics) , Nonassociative rings , Mathematics , Algebra , Field Theory and Polynomials , Commutative Rings and Algebras , Associative Rings and Algebras , Non-associative Rings and Algebras
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Call number:SPRINGER-2002-9783540456254:ONLINE Show nearby items on shelf
Title:Manis Valuations and Prüfer Extensions I A New Chapter in Commutative Algebra
Author(s): Manfred Knebusch
Date:2002
Size:1 online resource (274 p.)
Note:10.1007/b84018
Contents:Introduction -- Basics on Manis valuations and Prüfer extensions -- Multiplicative ideal theory -- PM-valuations and valuations of weaker type -- Appendix A: Flat epimorphisms -- Appendix B: Arithmetical rings -- Appendix C: A direct
proof of the existence of Manis valuation hulls -- References -- Index
ISBN:9783540456254
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Lecture Notes in Mathematics: 1791
Keywords: Mathematics , Algebraic geometry , Commutative algebra , Commutative rings , Mathematics , Commutative Rings and Algebras , Algebraic Geometry
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Call number:SPRINGER-2002-9783540454236:ONLINE Show nearby items on shelf
Title:Yetter-Drinfel’d Hopf Algebras over Groups of Prime Order
Author(s): Yorck Sommerhäuser
Date:2002
Size:1 online resource (164 p.)
Note:10.1007/b83955
Contents:Introduction -- Preliminaries -- Clifford theory -- Examples -- Isomorphisms -- Constructions -- Commutative Yetter-Drinfel'd Hopf algebras -- 7.Cocommutative Yetter-Drinfel'd Hopf algebras -- Semisimple Hopf algebras of dimension p3
-- Semisimple Hopf algebras of dimension pq -- Applications -- References -- Subject index -- Symbol index
ISBN:9783540454236
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Lecture Notes in Mathematics: 1789
Keywords: Mathematics , Associative rings , Rings (Algebra) , Mathematics , Associative Rings and Algebras
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Call number:SPRINGER-2002-9781461300410:ONLINE Show nearby items on shelf
Title:Algebra
Author(s): Serge Lang
Date:2002
Edition:Revised Third Edition
Size:1 online resource (914 p.)
Note:10.1007/978-1-4613-0041-0
Contents:One The Basic Objects of Algebra -- I Groups -- II Rings -- III Modules -- IV Polynomials -- Two Algebraic Equations -- V Algebraic Extensions -- VI Galois Theory -- VII Extensions of Rings -- VIII Transcendental Extensions -- IX
Algebraic Spaces -- X Noetherian Rings and Modules -- XI Real Fields -- XII Absolute Values -- Three Linear Algebra and Representations -- XIII Matrices and Linear Maps -- XIV Representation of One Endomorphism -- XV Structure of
Bilinear Forms -- XVI The Tensor Product -- XVII Semisimplicity -- XVIII Representations of Finite Groups -- XIX The Alternating Product -- Four Homological Algebra -- XX General Homology Theory -- XXI Finite Free Resolutions --
Appendix 2 Some Set Theory
ISBN:9781461300410
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Graduate Texts in Mathematics: 211
Keywords: Mathematics , Algebra , Associative rings , Rings (Algebra) , Commutative algebra , Commutative rings , Group theory , Matrix theory , Mathematics , Algebra , Commutative Rings and Algebras , Linear and Multilinear Algebras, Matrix Theory , Associative Rings and Algebras , Group Theory and Generalizations
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Call number:SPRINGER-2001-9789401006521:ONLINE Show nearby items on shelf
Title:Serial Rings
Author(s): Gennadi Puninski
Date:2001
Size:1 online resource (226 p.)
Note:10.1007/978-94-010-0652-1
Contents:1 Basic Notions -- 1.1 Preliminaries -- 1.2 Dimensions -- 1.3 Basic ring theory -- 1.4 Serial rings and modules -- 1.5 Ore sets -- 1.6 Semigroup rings -- 2 Finitely Presented Modules over Serial Rings -- 3 Prime Ideals in Serial Rings
-- 4 Classical Localizations in Serial Rings -- 5 Serial Rings with the A.C.C. on annihilators and Nonsingular Serial Rings -- 5.1 Serial rings with a.c.c. on annihilators -- 5.2 Nonsingular serial rings -- 6 Serial Prime Goldie Rings
-- 7 Noetherian Serial Rings -- 8 Artinian Serial Rings -- 8.1 General theory -- 8.2 d-rings and group rings -- 9 Serial Rings with Krull Dimension -- 10 Model Theory for Modules -- 11 Indecomposable Pure Injective Modules over Serial
Rings -- 12 Super-Decomposable Pure Injective Modules over Commutative Valuation Rings -- 13 Pure Injective Modules over Commutative Valuation Domains -- 14 Pure Projective Modules over Nearly Simple Uniserial Domains -- 15 Pure
Projective Modules over Exceptional Uniserial Rings -- 16 ?-Pure Injective Modules over Serial Rings -- 17 Endomorphism Rings of Artinian Modules -- Notations
ISBN:9789401006521
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Algebra , Associative rings , Rings (Algebra) , Mathematical logic , Mathematics , Associative Rings and Algebras , Algebra , Mathematical Logic and Foundations , Mathematics, general
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Call number:SPRINGER-2001-9783540446255:ONLINE Show nearby items on shelf
Title:Non-Semisimple Topological Quantum Field Theories for 3-Manifolds with Corners
Author(s): Thomas Kerler
Date:2001
Size:1 online resource (383 p.)
Note:10.1007/b82618
Contents:and Summary of Results -- The Double Category of Framed, Relative 3-Cobordisms -- Tangle-Categories and Presentation of Cobordisms -- Isomorphism between Tangle and Cobordism Double Categories -- Monoidal categories and monoidal
2-categories -- Coends and construction of Hopf algebras -- Construction of TQFT-Double Functors -- Generalization of a modular functor -- From Quantum Field Theory to Axiomatics -- Double Categories and Double Functors -- Thick
tangles
ISBN:9783540446255
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Lecture Notes in Mathematics: 1765
Keywords: Mathematics , Category theory (Mathematics) , Homological algebra , Commutative algebra , Commutative rings , Manifolds (Mathematics) , Complex manifolds , Physics , Mathematics , Commutative Rings and Algebras , Category Theory, Homological Algebra , Manifolds and Cell Complexes (incl. Diff.Topology) , Theoretical, Mathematical and Computational Physics
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Call number:SPRINGER-2001-9781461513070:ONLINE Show nearby items on shelf
Title:Multi-Valued Fields
Author(s): Yuri L Ershov
Date:2001
Size:1 online resource (270 p.)
Note:10.1007/978-1-4615-1307-0
Contents:1. Valuation Rings -- 1.1. Valuation Rings and Valuations of Fields -- 1.2. Valuation Rings in Algebraic Extensions -- 1.3. Henselian Valuation Rings -- 1.4. Alebgraic Extensions of Valued Fields -- 1.5. Immediate Extensions -- 1.6.
Density -- 1.7. Constructions -- 2. Multi-Valued Fields -- 2.1. Prüfer Rings -- 2.2. The Zariski Topology and the Restriction Mapping -- 2.3. Affine Families of Valuation Rings -- 2.4. Weakly Boolean Families and Boolean Families of
Valuation Rings -- 2.5. Near Boolean Families of Valuation Rings -- 2.6. Independence -- 3. Local-Global Properties of Near Boolean Families -- 3.1. Rational Points over Henselian Fields -- 3.2. Arithmetic Local-Global Principle --
3.3. Equivalent Forms of Property LGA -- 3.4. Preservation of Property LGA under Algebraic Separable Extensions -- 3.5. Geometric Local-Global Principle -- 3.6. Existence of Families with Property LGA -- 4. Model-Theoretic Properties
of Multi-Valued Fields -- 4.1. Embedding Theorems -- 4.2. The Robinson Theorem -- 4.3. Valued Fields -- 4.4. Finitely Multi-Valued Fields -- 4.5. Multi-Valued Fields with Boolean Families -- 4.6. Multi-Valued Fields with Near Boolean
Families -- Bibliographical and Historical Remarks -- References
ISBN:9781461513070
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Algebra , Commutative algebra , Commutative rings , Field theory (Physics) , Mathematical logic , Mathematics , Algebra , Field Theory and Polynomials , Commutative Rings and Algebras , Mathematical Logic and Foundations
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Call number:SPRINGER-2000-9789401595889:ONLINE Show nearby items on shelf
Title:Lattice Concepts of Module Theory
Author(s): Grigore Călugăreanu
Date:2000
Size:1 online resource (225 p.)
Note:10.1007/978-94-015-9588-9
Contents:1 Basic notions and results -- 2 Compactly generated lattices -- 3 Composition series. Decompositions -- 4 Essential elements. Pseudo—complements -- 5 Socle. Torsion lattices -- 6 Independence. Semiatomic lattices -- 7 Radical.
Superfluous and fully invariant elements -- 8 Lattices of finite uniform dimension -- 9 Purity and neatness in lattices -- 10 Coatomic lattices -- 11 Co—compact lattices -- 12 Supplemented lattices. Locally artinian lattices -- 13
Several dimensions -- 14 Solutions of exercises
ISBN:9789401595889
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Springer Texts in the Mathematical Sciences, A Graduate-Level Book Series: 22
Keywords: Mathematics , Algebra , Associative rings , Rings (Algebra) , Commutative algebra , Commutative rings , Group theory , Ordered algebraic structures , Mathematics , Order, Lattices, Ordered Algebraic Structures , Group Theory and Generalizations , Associative Rings and Algebras , Commutative Rings and Algebras , Algebra
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Call number:SPRINGER-2000-9783662126226:ONLINE Show nearby items on shelf
Title:Octonions, Jordan Algebras and Exceptional Groups
Author(s): Tonny A Springer
Date:2000
Size:1 online resource (208 p.)
Note:10.1007/978-3-662-12622-6
Contents:1. Composition Algebras -- 2. The Automorphism Group of an Octonion Algebra -- 3. Triality -- 4. Twisted Composition Algebras -- 5. J-algebras and Albert Algebras -- 6. Proper J-algebras and Twisted Composition Algebras -- 7.
Exceptional Groups -- 8. Cohomological Invariants
ISBN:9783662126226
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Commutative algebra , Commutative rings , Group theory , Mathematics , Commutative Rings and Algebras , Group Theory and Generalizations
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Call number:SPRINGER-2000-9783662041666:ONLINE Show nearby items on shelf
Title:Formal Power Series and Algebraic Combinatorics 12th International Conference, FPSAC’00, Moscow, Russia, June 2000, Proceedings
Author(s):
Date:2000
Size:1 online resource (808 p.)
Note:10.1007/978-3-662-04166-6
Contents:Exact Asymptotics of Meander Numbers -- Algorithms of Integral Representation of Combinatorial Sums and Their Applications -- Quasi-Symmetric Functions -- Equations over Free and Fully Residually Free Groups -- Recurring Sequences --
On Modules Supported in the Nullcone -- Towards Topological Classification of Univariate Complex Polynomials -- Applicability of Zeilberger’s Algorithm to Rational Functions -- Bases explicites et conjecture n! -- A Generalized Cover
Time for Random Walks on Graphs -- On the Square Root of Languages -- A General Cyclic Lemma for Multiset Permutation Inversions -- Enumeration of Some Labelled Trees -- On Aperiodic and Star-free Formal Power Series in Partially
Commuting Variables -- Some Generalizations of Quasi-symmetric Functions and Noncommutative Symmetric Functions -- The Skeleton of a Reduced Word and a Correspondence of Edelman and Greene -- Analytic Combinatorics of Chord Diagrams --
Specifying 2-trees -- About the Dynamics of Some Systems Based on Integer Partitions and Compositions -- Hecke Algebras of Type A at q = 0 and Quasi-differential Operators -- Central Characters and Conjugacy Classes of the Symmetric
Group -- The Füredi-Hajnal Conjecture Implies the Stanley-Wilf Conjecture -- Generalized Integer Partitions, Tilings of Zonotopes and Lattices -- Topology of Colors -- The Number of Subgroups in the Fundamental Groups of Some
Non-orientable 3-Manifolds -- Unranking of Labelled Combinatorial Structures -- On Gelfand-Tsetlin Bases for Representations of Classical Lie Algebras -- A Common Asymptotic Behavior for Different Classes of Sparse Labelled Graphs with
Given Number of Vertices and Edges -- On Functions Which are Limits of Domino Tilings -- Jeux de tableaux -- The Kronecker Product of Schur Functions Indexed by Two-Row Shapes or Hook Shapes -- Special Formal Series Solutions of Linear
Ordinary Differential Equations -- New Expressions for Level-restricted Kostka Polynomials -- A Combinatorial Interpretation of the Quotient-Difference Algorithm -- Regular Unicellular Dessins d’Enfants and Weil Curves -- Quantum
Division Ring -- On the Integer Models of Plane Trees -- Congruences Compatible with the Shuffle Product -- Arithmetical Properties of [pk]-Series Associated to p-Typical Formal Group Laws and Applications -- A Note on Linear
Preservers of a Certain Matrix Partial Order -- Trees of Diameter 4 -- The Makar-Limanov’s Construction of Algebraically Closed Skew Field via Mal’cev—Newmann Series -- About Nilpotency of Engel Algebras -- Belyi Functions Related to
Plane Graphs: Multiplicities and Parasitic Solutions -- Construction of the Annihilator of a Linear Recurring Sequence over Finite Module with the help of the Berlekamp—Massey Algorithm -- Polylinear Recurring Sequences over a Bimodule
-- An Improved Version of Standard Bases -- Effective Matrix Methods in Commutative Domains -- Polylinear Shift Registers and Standard Bases -- Burnside Matrices and Subgroup Embeddings in Finite Groups -- Distribution of Elements on
Cycles of Linear Recurrences over Galois Field -- On Witt’s Formula and Invariants for Free Lie Superalgebras -- Gröbner-Shirshov Bases for Kac-Moody Algebras An(1) and Bn(1) -- On Some Classes of Linear Representable Matroids -- On a
Class of Families of Belyi Functions -- Finite Basis Property of S-Ideals of Finite Dimensional Forms -- Peak Reduction Technique in Commutative Algebra -- On Algebraic Degrees and Multiplicities for Parameters of Some Finite Group
Rings -- Some Ring and Module Properties of Skew Power Series -- Some Ring and Module Properties of Skew Laurent Series -- Extending a Partially Ordered Set: Links with its Lattice of Ideals -- From Rational Functions to Regular
Languages -- Proving a Class of Hypergeometric Identities by Means of Generating Functions -- Séries génératrices exponentielles pour les ECO-systèmes signés -- New Statistics on Non-crossing Trees -- Expected Number of Inversions
After a Sequence of Random Adjacent Transpositions -- The Variety of Associative Rings, Which Satisfy the Identity x32 = 0, is Not Specht -- Polynomials of Bounded Tree Width -- Permutations Containing and Avoiding Certain Patterns --
On the Center of the Quantum Pseudoplactic Algebra -- ECO-Approximation of Algebraic Functions -- Methods for Computing the Concurrency Degree of Commutation Monoids -- An Application of Dumont’s Statistic -- On Wohlfahrt Formula for
Finite Abelian Groups -- Induction and Auslander-Reiten Sequences Over Crossed Products -- On Acceleration of Multiprecision Computation of Products and Sums of Products of Rational Numbers -- Combinatorial Aspects of Capelli
Identities and Structure of Algebras -- Generators and the Template Method Pattern. A Paradigm for Combinatorial Experimentation -- A Software to Solve Strip Tiling Problems -- Author Index
ISBN:9783662041666
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Computer science , Discrete mathematics , Combinatorics , Mathematics , Discrete Mathematics , Combinatorics , Mathematics of Computing
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Call number:SPRINGER-2000-9783034884402:ONLINE Show nearby items on shelf
Title:Polynomial Automorphisms and the Jacobian Conjecture
Author(s): Arno van den Essen
Date:2000
Size:1 online resource (329 p.)
Note:10.1007/978-3-0348-8440-2
Contents:I Methods -- 1. Preliminaries -- 2 Derivations and polynomial automorphisms -- 3 Invertibility criteria and inversion formulae -- 4 Injective morphisms -- 5 The tame automorphism group of a polynomial ring -- 6 Stabilization Methods
-- 7 Polynomial maps with nilpotent Jacobian -- II Applications -- 8 Applications of polynomial mappings to dynamical systems -- 9 Group actions -- 10 The Jacobian Conjecture -- III Appendices -- A Some commutative algebra -- A.1 Rings
-- A.2 Modules -- A.3 Localization -- A.4 Completions -- A.5 Finiteness conditions and integral extensions -- A.6 The universal coefficients method -- B Some basic results from algebraic geometry -- B.1 Algebraic sets -- B.2 Morphisms
of irreducible affine algebraic varieties -- C Some results from Gröbner basis theory -- C.1 Definitions and basic properties -- C.2 Applications: several algorithms -- D Flatness -- D.1 Flat modules and algebras -- D.2 Flat morphisms
between affine algebraic varieties -- E.2 Direct and inverse images -- F Special examples and counterexamples -- Authors Index
ISBN:9783034884402
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Progress in Mathematics : 190
Keywords: Mathematics , Algebra , Mathematics , Algebra
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Call number:SPRINGER-2000-9781475731804:ONLINE Show nearby items on shelf
Title:Non-Noetherian Commutative Ring Theory
Author(s):
Date:2000
Size:1 online resource (480 p.)
Note:10.1007/978-1-4757-3180-4
Contents:1 GCD Domains, Gauss’ Lemma, and Contents of Polynomials -- 2 The Class Group and Local Class Group of an Integral Domain -- 3 Mori Domains -- 4 What’s New About Integer-Valued Polynomials on a Subset? -- 5 Half-Factorial Domains, a
Survey -- 6 On Generalized Lengths of Factorizations in Dedekind and Krull Domains -- 7 Recent Progress on Going-Down I -- 8 Localizing Systems and Semistar Operations -- 9 Ideal Theory in Pullbacks -- 10 Commutative Rings of Dimension
0 -- 11 Finite Conductor Rings with Zero Divisors -- 12 Construction of Ideal Systems with Nice Noetherian Properties -- 13 Generalized Local Rings and Finite Generation of Powers of Ideals -- 14 Connecting Trace Properties -- 15
Constructing Examples of Integral Domains by Intersecting Valuation Domains -- 16 Examples Built With D+M, A+XB[X] and Other Pullback Constructions -- 17 T-Closedness -- 18 E-rings and Related Structures -- 19 Prime Ideals and
Decompositions of Modules -- 20 Putting t-Invertibility to Use -- 21 One Hundred Problems in Commutative Ring Theory
ISBN:9781475731804
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Mathematics and Its Applications : 520
Keywords: Mathematics , Algebraic geometry , Commutative algebra , Commutative rings , Algebra , Field theory (Physics) , Mathematics , Commutative Rings and Algebras , Field Theory and Polynomials , Algebraic Geometry
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Call number:SPRINGER-1998-9789401590044:ONLINE Show nearby items on shelf
Title:Exercises in Basic Ring Theory
Author(s): Grigore Cǎlugǎreanu
Date:1998
Size:1 online resource (200 p.)
Note:10.1007/978-94-015-9004-4
Contents:I Exercises -- 1 Fundamentals -- 2 Ideals -- 3 Zero Divisors -- 4 Ring Homomorphisms -- 5 Characteristics -- 6 Divisibility in Integral Domains -- 7 Division Rings -- 8 Automorphisms -- 9 The Tensor Product -- 10 Artinian and
Noetherian Rings -- 11 Socle and Radical -- 12 Semisimple Rings -- 13 Prime Ideals, Local Rings -- 14 Polynomial Rings -- 15 Rings of Quotients -- 16 Rings of Continuous Functions -- 17 Special Problems -- II Solutions -- 1
Fundamentals -- 2 Ideals -- 3 Zero Divisors -- 4 Ring Homomorphisms -- 5 Characteristics -- 6 Divisibility in Integral Domains -- 7 Division Rings -- 8 Automorphims -- 9 The Tensor Product -- 10 Artinian and Noetherian Rings -- 11
Socle and Radical -- 12 Semisimple Rings -- 13 Prime Ideals, Local Rings -- 14 Polynomial Rings -- 15 Rings of Quotients -- 16 Rings of Continuous Functions -- 17 Special problems
ISBN:9789401590044
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Kluwer Texts in the Mathematical Sciences, A Graduate-Level Book Series: 20
Keywords: Mathematics , Associative rings , Rings (Algebra) , Commutative algebra , Commutative rings , Algebra , Field theory (Physics) , Ordered algebraic structures , Topology , Mathematics , Associative Rings and Algebras , Commutative Rings and Algebras , Field Theory and Polynomials , Order, Lattices, Ordered Algebraic Structures , Topology
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Call number:SPRINGER-1998-9789401153089:ONLINE Show nearby items on shelf
Title:Algebraic Groups and their Representations
Author(s):
Date:1998
Size:1 online resource (374 p.)
Note:10.1007/978-94-011-5308-9
Contents:Linear and nonlinear group actions, and the Newton Institute program -- Tilting modules for algebraic groups -- Semisimplicity in positive characteristic -- Homology bases arising from reductive groups over a finite field -- Highest
weight modules associated to parabolic subgroups with commutative unipotent radicals -- Symmetric groups and Schur algebras -- Branching rules for symmetric groups and applications -- Endomorphism algebras and representation theory --
Representations of simple Lie algebras: modern variations on a classical theme -- The path model, the quantum Frobenius map and standard monomial theory -- Arithmetical properties of blocks -- The isomorphism and isogeny theorems for
reductive algebraic groups -- Double cosets in algebraic groups -- Dense orbits and double cosets -- Subgroups of exceptional groups -- Overgroups of special elements in simple algebraic groups and finite groups of Lie type -- Some
applications of subgroup structure to probabilistic generation and covers of curves -- Quasithin groups -- Tame groups of odd and even type
ISBN:9789401153089
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:NATO ASI Series, Series C: Mathematical and Physical Sciences: 517
Keywords: Mathematics , Group theory , Nonassociative rings , Rings (Algebra) , Topological groups , Lie groups , Mathematics , Topological Groups, Lie Groups , Group Theory and Generalizations , Non-associative Rings and Algebras
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Call number:SPRINGER-1998-9789401150866:ONLINE Show nearby items on shelf
Title:Semidistributive Modules and Rings
Author(s): Askar A Tuganbaev
Date:1998
Size:1 online resource (357 p.)
Note:10.1007/978-94-011-5086-6
Contents:1 Radicals, local and semisimple modules -- 1.1 Maximal submodules and the Jacobson radical -- 1.2 Local and uniserial modules -- 1.3 Semisimple and Artinian modules -- 1.4 The prime radical -- 2 Projective and injective modules --
2.1 Free and projective modules -- 2.2 Injective modules -- 2.3 Injective hull -- 3 Bezout and regular modules -- 3.1 Regular modules -- 3.2 Unit-regular rings -- 3.3 Semilocal rings and distributivity -- 3.4 Strongly regular rings --
3.5 Bezout rings -- 4 Continuous and finite-dimensional modules -- 4.1 Closed submodules -- 4.2 Continuous modules -- 4.3 Finile-dimensional modules -- 4.4 Nonsingular ?-injective modules -- 5 Rings of quotients -- 5.1 Ore sets -- 5.2
Denominator sets and localizable rings -- 5.3 Maximal rings of quotients -- 6 Flat modules and semiperfect rings -- 6.1 Characterizations of flat modules -- 6.2 Submodules of flat modules -- 6.3 Semiperfect and perfect rings -- 7
Semihereditary and invariant rings -- 7.1 Coherent and reduced rings -- 7.2 Invariant rings -- 7.3 Rings with integrally closed factor rings -- 8 Endomorphism rings -- 8.1 Modules over endomorphism rings and quasi injective modules --
8.2 Nilpotent endomorphisms -- 8.3 Strongly indecomposable modules -- 9 Distributive rings with maximum conditions -- 9.1 Arithmetics of ideals -- 9.2 Noel.herian rings -- 9.3 Classical rings of quotients of distributive rings -- 9.4
Rings algebraic over their centre -- 10 Self-injective and skew-injective rings -- 10.1 Quasi-frobenius rings and direct sums of injective modules -- 10.2 Cyclic ?-injective modules -- 10.3 Integrally closed Noetherian rings -- 10.4
Cyclic skew-injective modules -- 10.5 Countably injective rings -- 11 Semidistributive and serial rings -- 11.1 Semidistributive modules -- 11.2 Semidistributive rings -- 11.3 Serial modules and rings -- 12 Monoid rings and related
topics -- 12.1 Series and polynomial rings -- 12.2 Quaternion algebras -- 12.3 Subgroups, submonoids, and annihilators -- 12.4 Regular group rings -- 12.5 Cancellative monoids -- 12.6 Semilattices and regular monoids
ISBN:9789401150866
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Mathematics and Its Applications : 449
Keywords: Mathematics , Associative rings , Rings (Algebra) , Commutative algebra , Commutative rings , Mathematics , Associative Rings and Algebras , Commutative Rings and Algebras
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Call number:SPRINGER-1998-9789401150729:ONLINE Show nearby items on shelf
Title:Algebra and Operator Theory Proceedings of the Colloquium in Tashkent, 1997
Author(s):
Date:1998
Size:1 online resource (250 p.)
Note:10.1007/978-94-011-5072-9
Contents:On Leibniz Algebras -- A Moduli Problem Related to Complex Supermanifolds -- Comparaison de l’Homologie de Hochschild et de l’Homologie de Poisson pour une déformation des surfaces de Klein -- Quelques résultats en K-Théorie réelle --
Some Nilpotent Lie Algebras and its Applications -- Algèbres de Lie rigides -- Family of p-Filiform Lie Algebras -- The Functional Representation of Commutative Symmetric Operator Algebras in Pontryagin Space -- Continuous
Decomposition of Real Von Neumann Algebras of Type III -- Espaces vectoriels différentiels -- Complétude de l’équation d’Euler -- On Invariants of Second Order Linear Partial Differential Equations in two Variables -- Lattice-Ordered
Groupoids and their Prime Spectrums -- Sur un problème d’Elie Cartan -- Classification of Non-Commutative Arens Algebras Associated with Semi-Finite Traces -- Order Unit Space of Type In with Banach Ball Property -- On Markov Random
Fields on UHF Algebras -- Injectivity, Amenability, Semi Discreteness and Hyperfiniteness in Real W*-Algebras -- Contractive Projections on Facially Symmetric Spaces -- The Property (t?) for Locally Compact Connected groups -- Grupos
Cuánticos -- On the Group of Weak Automorphisms of a Family of Equivalence Relations
ISBN:9789401150729
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Algebraic geometry , Nonassociative rings , Rings (Algebra) , Operator theory , Differential geometry , Physics , Mathematics , Non-associative Rings and Algebras , Operator Theory , Algebraic Geometry , Differential Geometry , Theoretical, Mathematical and Computational Physics
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Call number:SPRINGER-1998-9781461217947:ONLINE Show nearby items on shelf
Title:Introduction to Liaison Theory and Deficiency Modules
Author(s): Juan C Migliore
Date:1998
Size:1 online resource (218 p.)
Note:10.1007/978-1-4612-1794-7
Contents:1 Background -- 1.1 Finitely Generated Graded S-Modules -- 1.2 The Deficiency Modules (Mi)(V) -- 1.3 Hyperplane and Hypersurface Sections -- 1.4 Artinian Reductions and h-Vectors -- 1.5 Examples -- 2 Submodules of the Deficiency
Module -- 2.1 Measuring Deficiency -- 2.2 Generalizing Dubreil’s Theorem -- 2.3 Lifting the Cohen-Macaulay Property -- 3 Buchsbaum Curves and Liaison Addition -- 3.1 Buchsbaum Curves -- 3.2 Liaison Addition -- 3.3 Constructing
Buchsbaum Curves in P3 -- 4 Gorenstein Subschemes of Projective Space -- 4.1 Basic Results on Gorenstein Ideals -- 4.2 Constructions of Gorenstein Schemes -- 4.3 Codimension Three Gorenstein Ideals -- 5 Liaison Theory in Arbitrary
Codimension -- 5.1 Definitions and First Examples -- 5.2 Relations Between Linked Schemes -- 5.3 The Hartshorne-Schenzel Theorem -- 5.4 The Structure of an Even Liaison Class -- 5.5 Geometric Invariants of a Liaison Class -- 6 Liaison
Theory in Codimension Two -- 6.1 The aCM Situation and Generalizations -- 6.2 Rao’s Results -- 6.3 The Lazarsfeld-Rao Property -- 6.4 Applications
ISBN:9781461217947
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Progress in Mathematics : 165
Keywords: Mathematics , Algebra , Algebraic geometry , Commutative algebra , Commutative rings , Mathematics , Algebraic Geometry , Commutative Rings and Algebras , Algebra
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Call number:SPRINGER-1998-9781447104254:ONLINE Show nearby items on shelf
Title:Groups, Rings and Fields
Author(s): D. A. R Wallace
Date:1998
Size:1 online resource (248 p.)
Note:10.1007/978-1-4471-0425-4
Contents:1 Sets and Mappings -- 2 The Integers -- 3 Introduction to Rings -- 4 Introduction to Groups -- 5 Rings -- 6 Topics in Group Theory -- Hints to Solutions -- Suggestions for Further Study
ISBN:9781447104254
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Algebra , Commutative algebra , Commutative rings , Mathematics , Algebra , Commutative Rings and Algebras
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Call number:SPRINGER-1997-9789401724364:ONLINE Show nearby items on shelf
Title:Non-Commutative Valuation Rings and Semi-Hereditary Orders
Author(s): Hidetoshi Marubayashi
Date:1997
Size:1 online resource (192 p.)
Note:10.1007/978-94-017-2436-4
Contents:I. Semi-Hereditary and Prüfer Orders -- II. Dubrovin Valuation Rings -- III. Semi-Local Bezout Orders -- IV. The Applications and Examples -- A1. Semi-perfect rings and serial rings -- A2. Coherent rings -- A3. Azumaya algebras -- A4.
The lifting idempotents -- A5. Wedderburn’s Theorem -- References -- Index of Notation
ISBN:9789401724364
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:K-Monographs in Mathematics: 3
Keywords: Mathematics , Associative rings , Rings (Algebra) , Category theory (Mathematics) , Homological algebra , Commutative algebra , Commutative rings , Algebra , Field theory (Physics) , Ordered algebraic structures , Mathematics , Associative Rings and Algebras , Order, Lattices, Ordered Algebraic Structures , Category Theory, Homological Algebra , Commutative Rings and Algebras , Field Theory and Polynomials
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Call number:SPRINGER-1997-9789401156400:ONLINE Show nearby items on shelf
Title:Ordered Algebraic Structures Proceedings of the Curaçao Conference, sponsored by the Caribbean Mathematics Foundation, June 26–30, 1995
Author(s):
Date:1997
Size:1 online resource (332 p.)
Note:10.1007/978-94-011-5640-0
Contents:A Survey of f-Rings and some of their Generalizations -- Reflections on the Global Dimensions of Rings of Continuous Functions -- Continuous Ultraproducts -- Actions on Archimedean Lattice-Ordered Groups with Strong Unit -- Pointfree
Topology and the Spectra of f-Rings -- Commutative Singular f-Rings -- Torsion Classes of Lattice-Ordered Groups with Invariant Radicals -- The Automorphism Groups of Hahn Groups -- The Laterally ?-Complete Reflection of an Archimedean
Lattice-Ordered Group -- Ax-Kochen-Ershov Principles for Valued and Ordered Vector Spaces -- Quasi-normal f-Rings -- Rings of Continuous Functions as Real Closed Rings -- On Universal Words for Automorphism Groups of Linear Orders
ISBN:9789401156400
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Category theory (Mathematics) , Homological algebra , Commutative algebra , Commutative rings , Algebra , Ordered algebraic structures , Mathematical logic , Topology , Mathematics , Order, Lattices, Ordered Algebraic Structures , Topology , Category Theory, Homological Algebra , Commutative Rings and Algebras , Mathematical Logic and Foundations
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Call number:SPRINGER-1997-9783540695981:ONLINE Show nearby items on shelf
Title:Projective Modules and Complete Intersections
Author(s): Satya Mandal
Date:1997
Size:1 online resource (124 p.)
Note:10.1007/BFb0093556
Contents:Preliminaires -- Patching modules and other preliminaries -- Extended modules over polynomial rings -- Modules over commutative rings -- The theory of matrices -- Complete intersections -- The techniques of lindel
ISBN:9783540695981
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Lecture Notes in Mathematics: 1672
Keywords: Mathematics , Commutative algebra , Commutative rings , Mathematics , Commutative Rings and Algebras
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Call number:SPRINGER-1997-9781461219781:ONLINE Show nearby items on shelf
Title:Advances in Ring Theory
Author(s):
Date:1997
Size:1 online resource (335 p.)
Note:10.1007/978-1-4612-1978-1
Contents:Kasch Modules -- Compactness in Categories and Interpretations -- A Ring of Morita Context in Which Each Right Ideal is Weakly Self-injective -- Splitting Theorems and a Problem of Müller -- Decompositions of D1 Modules -- Right Cones
in Groups -- On Extensions of Regular Rings of Finite Index by Central Elements -- Intersections of Modules -- Minimal Cogenerators Over Osofsky and Camillo Rings -- Uniform Modules Over Goldie Prime Serial Rings -- Co-Versus
Contravariant Finiteness of Categories of Representations -- Monomials and the Lexicographic Order -- Rings Over Which Direct Sums of CS Modules Are CS -- Exchange Properties and the Total -- Local Bijective Gabriel Correspondence and
Torsion Theoretic FBN Rings -- Normalizing Extensions and the Second Layer Condition -- Generators of Subgroups of Finite Index in GLm (?G) -- Weak Relative Injective M-Subgenerated Modules -- Direct Product and Power Series Formations
Over 2-Primal Rings -- Localization in Noetherian Rings -- Projective Dimension of Ideals in Von Neumann Regular Rings -- Homological Properties of Color Lie Superalgebras -- Indecomposable Modules Over Artinian Right Serial Rings --
Nonsingular Extending Modules -- Right Hereditary, Right Perfect Rings Are Semiprimary -- On the Endomorphism Ring of a Discrete Module: A Theorem of F. Kasch -- Nonsingular Rings with Finite Type Dimension
ISBN:9781461219781
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Algebra , Associative rings , Rings (Algebra) , Commutative algebra , Commutative rings , Mathematics , Commutative Rings and Algebras , Associative Rings and Algebras , General Algebraic Systems , Algebra
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Call number:SPRINGER-1996-9783642770302:ONLINE Show nearby items on shelf
Title:General Topology II Compactness, Homologies of General Spaces
Author(s):
Date:1996
Size:1 online resource (256 p.)
Note:10.1007/978-3-642-77030-2
Contents:§1. Compactness and Its Different Forms: Separation Axioms -- 1.1. Different Definitions of Compactness -- 1.2. Relative Compactness -- 1.3. Countable Compactness -- 1.4. Relative Countable Compactness -- 1.5. Pseudocompact Spaces --
1.6. Separation Axioms and Properties Related to Compactness -- 1.7. Star Characterizations of Countable Compactness and Pseudocompactness -- §2. Compactness and Products -- 2.1. Tikhonov’s Theorem on Compactness of the Product -- 2.2.
Products of Countably Compact Spaces -- 2.3. Products of Pseudocompact Spaces -- 2.4. Total Countable Compactness and Total Pseudocompactness -- 2.5. Compactness with Respect to a Fixed Ultrafilter (?-Compactness) -- 2.6. ?-Products of
Compact Spaces -- §3. Continuous Mappings of Compact Spaces -- 3.1. Theorem on Compactness of the Image and Its Consequences -- 3.2. Continuous Images of “Standard” Compacta -- 3.3. Open Mappings of Compacta and Dimension -- 3.4.
Mardeši?’s Factorization Theorem -- 3.5. Continuous Images of Ordered Compacta -- 3.6. Pseudocompactness and Continuous Mappings -- 3.7. Continuous Mappings and Extremally Disconnected Compacta -- 3.8. Scattered Compacta and Their
Images -- §4. Metrizability Conditions for Compact, Countably Compact and Pseudocompact Spaces -- 4.1. Classical Results and the Theorem of Chaber -- 4.2. Theorems of Dow and Tkachenko -- 4.3. Point-countable and ?-Point-finite Bases
-- 4.4. Quasi-developments and ??-Bases -- 4.5. Strongly N0-Noetherian Bases -- 4.6. Rank of a Base and Metrizability Conditions for Compacta -- 4.7. Symmetrics and Metrizability of Compacta -- §5. Cardinal Invariants in the Class of
Compacta -- 5.1. Network Weight, Diagonal Number and Weight of Compacta -- 5.2. Pseudocharacter and Character in the Class of Compacta -- 5.3. First Countable Compacta -- 5.4. Perfectly Normal Compacta -- 5.5. Continuous Images of
First Countable Compacta -- 5.6. Sequential Compacta and the First Axiom of Countability Almost Everywhere -- 5.7. Corson Compact Spaces and N0-Monolithicity -- 5.8. Compacta of Countable Tightness -- 5.9. Mappings of Compacta onto
Tikhonov Cubes I? -- 5.10. Dyadic Compacta -- 5.11. Supercompacta and Extensions of the Class of Dyadic Compacta -- §6. Compact Extensions -- 6.1. General Remarks about Compact Extensions -- 6.2. Compact T1-Extensions -- 6.3. Embedding
Topological Spaces into Compact T1-Spaces of Countable Weight -- 6.4. Compact Hausdorff Extensions, Relation of Subordination -- 6.5. Compact Extensions of Locally Compact Hausdorff Spaces -- 6.6. Duality Between Properties of a Space
and of Its Remainder -- 6.7. Compact Extensions and Cardinal Invariants -- 6.8. Compact Hausdorff Extensions and Perfect Mappings -- 6.9. Properties of the ?ech-Stone Extension -- 6.10. Closing Remarks Concerning Compact Hausdorff
Extensions -- §7. Compactness and Spaces of Functions -- 7.1. Natural Topologies on Spaces of Functions -- 7.2. Joint Continuity and Compact-Open Topology -- 7.3. Stone-Weierstrass Theorem -- 7.4. Convex Compact Sets and Krein-Milman
Theorem -- 7.5. Theorem of Alaoglu and Convex Hulls of Compacta -- 7.6. Fixed-Point Theorems for Continuous Mappings of Convex Compacta -- 7.7. Milyutin Compact Spaces -- 7.8. Dugundji Compact Spaces -- §8. Algebraic Structures and
Compactness — A Review of the Most Important Results -- 8.1. Compacta and Ideals in Rings of Functions -- 8.2. Spectrum of a Ring. Zariski Topology -- 8.3. The Space of Maximal Ideals of a Commutative Banach Algebra -- 8.4. The Stone
Space of a Boolean Algebra -- 8.5. Pontryagin’s Duality Theory -- 8.6. Compact Extensions of Topological Groups. Almost Periodic Functions -- 8.7. Compacta and Namioka’s Theorem About Joint Continuity of Separately Continuous Functions
-- 8.8. Fragmentable and Strongly Fragmentable Compacta and Radon-Nikodým Compact Spaces -- 8.9. Hilbert Modules over C*-Algebras of Continuous Functions on Compacta -- 8.10. Compact Subsets of Topological Fields -- 8.11. Locally
Compact Topological Groups and Paracompactness -- 8.12. Final Remarks -- References
ISBN:9783642770302
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Encyclopaedia of Mathematical Sciences: 50
Keywords: Mathematics , K-theory , Topological groups , Lie groups , Algebraic topology , Mathematics , Algebraic Topology , Topological Groups, Lie Groups , K-Theory
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Call number:SPRINGER-1996-9780817644338:ONLINE Show nearby items on shelf
Title:Combinatorics and Commutative Algebra
Author(s): Richard P Stanley
Date:1996
Edition:Second Edition
Size:1 online resource (168 p.)
Note:10.1007/b139094
Contents:Background -- Nonnegative Integral Solutions to Linear Equations -- The Face Ring of a Simplicial Complex -- Further Aspects of Face Rings
ISBN:9780817644338
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Progress in Mathematics : 41
Keywords: Mathematics , Commutative algebra , Commutative rings , Topology , Combinatorics , Mathematics , Combinatorics , Commutative Rings and Algebras , Topology
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Call number:SPRINGER-1995-9789401585552:ONLINE Show nearby items on shelf
Title:Automorphisms of Affine Spaces Proceedings of a Conference held in Curaçao (Netherlands Antilles), July 4–8, 1994, under auspices of the Caribbean Mathematical Foundation (CMF)
Author(s):
Date:1995
Size:1 online resource (244 p.)
Note:10.1007/978-94-015-8555-2
Contents:I Polynomial Maps in Dimension n -- Seven Lectures on Polynomial Automorphisms -- The Jacobian Conjecture: Some Steps towards Solution -- Finite Automorphisms of Affine N-Space -- Polyomorphisms Conjugate to Dilations -- On Separable
Algebras over a U.F.D. and the Jacobian Conjecture in Any Characteristic -- Global Injectivity of Polynomial Maps Via Vector Fields -- II Two-dimensional Results -- On the Markus-Yamabe Conjecture -- Derivations Generated by
Polynomials, Their Images and Complements of the Images -- Normal Forms and the Jacobian Conjecture -- Radial Similarity of Newton Polygons -- An Algorithm that Determines whether a Polynomial Map is Bijective -- III Group Actions --
Algebraic Aspects of Additive Group Actions on Complex Affine Space -- Quotients of Algebraic Group Actions -- One-Parameter Subgroups and the Triangular Subgroup of the Affine Cremona Group -- A Note on Nagata’s Automorphism -- IV
Reactions on the conference -- On a Question of Yosef Stein -- A Counterexample to a Conjecture of Meisters -- Open Problems -- Some Conference Impressions
ISBN:9789401585552
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Algebraic geometry , Commutative algebra , Commutative rings , Differential equations , Partial differential equations , Algorithms , Mathematics , Algebraic Geometry , Commutative Rings and Algebras , Ordinary Differential Equations , Algorithms , Partial Differential Equations
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Call number:SPRINGER-1995-9789401104432:ONLINE Show nearby items on shelf
Title:Abelian Groups and Modules Proceedings of the Padova Conference, Padova, Italy, June 23–July 1, 1994
Author(s):
Date:1995
Size:1 online resource (517 p.)
Note:10.1007/978-94-011-0443-2
Contents:Dual relative Krull dimension of modules over commutative rings -- Morita duality, linear compactness and AB5*: a survey -- Near isomorphism of Butler groups and representations of finite posets -- Locally free finite rank Butler
groups and near isomorphism -- Subgroups of Butler groups -- Some abelian groups with free duals -- Confirmation of a conjecture of Dauns and Hofmann on biregular rings -- Induction functors for the Doi-Koppinen unified Hopf modules --
One-dimensional rings of finite representation type -- Uniqueness of dualities -- Classification and non-classification results for abelian groups -- ?-pure-injectivemodules over serial rings -- Modules over endomorphism rings as
homotopy classes -- Categories of mixed and torsion-free finite rank abelian groups -- Reflexive representations of algebras -- Zero-dimensional subrings of commutative rings -- The dimension of the tensor product of two particular
pullbacks -- On the existence of rigid ?1- free abelian groups of cardinality ?1 -- Warfield duality and module extensions over a noetherian domain -- Von Neumann regular rings and direct sum decomposition problems -- Selforthogonal
modules -- Subrings of finite-dimensional rings -- Primary abelian groups whose countable subgroups have countable closure -- Isotype separable subgroups of totally projective groups -- Representable preradicals with enough projectives
-- Rings with periodic unit groups -- Abelian groups with contractions II: Weak o-minimality -- Almost completely decomposable torsion-free abelian groups -- On the exchange property for quasi-continuous modules -- Endomorphism rings
of Reid groups -- Completely decomposable subgroups and factors of finite rank completely decomposable groups -- On the endomorphism ring of an infinite dimensional vector space -- Some algebraically compact modules I -- The near
endomorphism ring of an almost completely decomposable group -- Reflexivity of left serial algebras -- On a class of minimal topological modules -- Steady rings may contain large sets of orthogonal idempotents -- The Holy Grail of
Algebra: Seeking complete sets of invariants -- Invariants for almost completely decomposable groups -- A class of modules with semisimple behavior -- The finitistic dimension conjectures — a tale of 3.5 decades
ISBN:9789401104432
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Mathematics and Its Applications : 343
Keywords: Mathematics , Algebraic geometry , Associative rings , Rings (Algebra) , Category theory (Mathematics) , Homological algebra , Commutative algebra , Commutative rings , Group theory , Mathematics , Associative Rings and Algebras , Group Theory and Generalizations , Category Theory, Homological Algebra , Commutative Rings and Algebras , Algebraic Geometry
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Call number:SPRINGER-1995-9783642620294:ONLINE Show nearby items on shelf
Title:Homology
Author(s): Saunders Mac Lane
Date:1995
Size:1 online resource (422 p.)
Note:10.1007/978-3-642-62029-4
Contents:I. Modules, Diagrams, and Functors -- 1. The Arrow Notation -- 2. Modules -- 3. Diagrams -- 4. Direct Sums -- 5. Free and Projective Modules -- 6. The Functor Horn -- 7. Categories -- 8. Functors -- II. Homology of Complexes -- 1.
Differential Groups -- 2. Complexes -- 3. Cohomology -- 4. The Exact Homology Sequence -- 5. Some Diagram Lemmas -- 6. Additive Relations -- 7. Singular Homology -- 8. Homotopy -- 9. Axioms for Homology -- III. Extensions and
Resolutions -- 1. Extensions of Modules -- 2. Addition of Extensions -- 3. Obstructions to the Extension of Homomorphisms -- 4. The Universal Coefficient Theorem for Cohomology -- 5. Composition of Extensions -- 6. Resolutions -- 7.
Injective Modules -- 8. Injective Resolutions -- 9. Two Exact Sequences for Extn -- 10. Axiomatic Description of Ext -- 11. The Injective Envelope -- IV. Cohomology of Groups -- 1. The Group Ring -- 2. Crossed Homomorphisms -- 3. Group
Extensions -- 4. Factor Sets -- 5. The Bar Resolution -- 6. The Characteristic Class of a Group Extension -- 7. Cohomology of Cyclic and Free Groups -- 8. Obstructions to Extensions -- 9. Realization of Obstructions -- 10. SCHUR’S
Theorem -- 11. Spaces with Operators -- V. Tensor and Torsion Products -- 1. Tensor Products -- 2. Modules over Commutative Rings -- 3. Bimodules -- 4. Dual Modules -- 5. Right Exactness of Tensor Products -- 6. Torsion Products of
Groups -- 7. Torsion Products of Modules -- 8. Torsion Products by Resolutions -- 9. The Tensor Product of Complexes -- 10. The KÜNNETH Formula -- 11. Universal Coefficient Theorems -- VI. Types of Algebras -- 1. Algebras by Diagrams
-- 2. Graded Modules -- 3. Graded Algebras -- 4. Tensor Products of Algebras -- 5. Modules over Algebras -- 6. Cohomology of free Abelian Groups -- 7. Differential Graded Algebras -- 8. Identities on Horn and ? -- 9. Coalgebras and
HOPF Algebras -- VII. Dimension -- 1. Homological Dimension -- 2. Dimensions in Polynomial Rings -- 3. Ext and Tor for Algebras -- 4. Global Dimensions of Polynomial Rings -- 5. Separable Algebras -- 6. Graded Syzygies -- 7. Local
Rings -- VIII. Products -- 1. Homology Products -- 2. The Torsion Product of Algebras -- 3. A Diagram Lemma -- 4. External Products for Ext -- 5. Simplicial Objects -- 6. Normalization -- 7. Acyclic Models -- 8. The EILENBERG-ZILBER
Theorem -- 9. Cup Products -- IX. Relative Homological Algebra -- 1. Additive Categories -- 2. Abelian Categories -- 3. Categories of Diagrams -- 4. Comparison of Allowable Resolutions -- 5. Relative Abelian Categories -- 6. Relative
Resolutions -- 7. The Categorical Bar Resolution -- 8. Relative Torsion Products -- 9. Direct Products of Rings -- X. Cohomology of Algebraic Systems -- 1. Introduction -- 2. The Bar Resolution for Algebras -- 3. The Cohomology of an
Algebra -- 4. The Homology of an Algebra -- 5. Homology of Groups and Monoids -- 6. Ground Ring Extensions and Direct Products -- 7. Homology of Tensor Products -- 8. The Case of Graded Algebras -- 9. Complexes of Complexes -- 10.
Resolutions and Constructions -- 11. Two-stage Cohomology of DGA-Algebras -- 12. Cohomology of Commutative DGA-Algebras -- 13. Homology of Algebraic Systems -- XI. Spectral Sequences -- 1. Spectral Sequences -- 2. Fiber Spaces -- 3.
Filtered Modules -- 4. Transgression -- 5. Exact Couples -- 6. Bicomplexes -- 7. The Spectral Sequence of a Covering -- 8. Cohomology Spectral Sequences -- 9. Restriction, Inflation, and Connection -- 10. The Lyndon Spectral Sequence
-- 11. The Comparison Theorem -- XII. Derived Functors -- 1. Squares -- 2. Subobjects and Quotient Objects -- 3. Diagram Chasing -- 4. Proper Exact Sequences -- 5. Ext without Projectives -- 6. The Category of Short Exact Sequences --
7. Connected Pairs of Additive Functors -- 8. Connected Sequences of Functors -- 9. Derived Functors -- 10. Products by Universality -- 11. Proper Projective Complexes -- 12. The Spectral KÜNNETH Formula -- List of Standard Symbols
ISBN:9783642620294
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Classics in Mathematics: 114
Keywords: Mathematics , Category theory (Mathematics) , Homological algebra , Mathematics , Category Theory, Homological Algebra
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Call number:SPRINGER-1995-9781461253501:ONLINE Show nearby items on shelf
Title:Commutative Algebra with a View Toward Algebraic Geometry
Author(s): David Eisenbud
Date:1995
Size:1 online resource (788 p.)
Note:10.1007/978-1-4612-5350-1
Contents:Advice for the Beginner -- Information for the Expert -- Prerequisites -- Sources -- Courses -- Acknowledgements -- 0 Elementary Definitions -- 0.1 Rings and Ideals -- 0.2 Unique Factorization -- 0.3 Modules -- I Basic Constructions
-- 1 Roots of Commutative Algebra -- 2 Localization -- 3 Associated Primes and Primary Decomposition -- 4 Integral Dependence and the Nullstellensatz -- 5 Filtrations and the Artin-Rees Lemma -- 6 Flat Families -- 7 Completions and
Hensel’s Lemma -- II Dimension Theory -- 8 Introduction to Dimension Theory -- 9 Fundamental Definitions of Dimension Theory -- 10 The Principal Ideal Theorem and Systems of Parameters -- 11 Dimension and Codimension One -- 12
Dimension and Hilbert-Samuel Polynomials -- 13 The Dimension of Affine Rings -- 14 Elimination Theory, Generic Freeness, and the Dimension of Fibers -- 15Gröbner Bases -- 16 Modules of Differentials -- III Homological Methods -- 17
Regular Sequences and the Koszul Complex -- 18 Depth, Codimension, and Cohen-Macaulay Rings -- 19 Homological Theory of Regular Local Rings -- 20 Free Resolutions and Fitting Invariants -- 21 Duality, Canonical Modules, and Gorenstein
Rings -- Appendix 1 Field Theory -- A1.1 Transcendence Degree -- A1.2 Separability -- A1.3.1 Exercises -- Appendix 2 Multilinear Algebra -- A2.1 Introduction -- A2.2 Tensor Product -- A2.3 Symmetric and Exterior Algebras -- A2.3.1
Bases -- A2.3.2 Exercises -- A2.4 Coalgebra Structures and Divided Powers -- A2.5 Schur Functors -- A2.5.1 Exercises -- A2.6 Complexes Constructed by Multilinear Algebra -- A2.6.1 Strands of the Koszul Comple -- A2.6.2 Exercises --
Appendix 3 Homological Algebra -- A3.1 Introduction -- I: Resolutions and Derived Functors -- A3.2 Free and Projective Modules -- A3.3 Free and Projective Resolutions -- A3.4 Injective Modules and Resolutions -- A3.4.1 Exercises --
Injective Envelopes -- Injective Modules over Noetherian Rings -- A3.5 Basic Constructions with Complexes -- A3.5.1 Notation and Definitions -- A3.6 Maps and Homotopies of Complexes -- A3.7 Exact Sequences of Complexes -- A3.7.1
Exercises -- A3.8 The Long Exact Sequence in Homology -- A3.8.1 Exercises -- Diagrams and Syzygies -- A3.9 Derived Functors -- A3.9.1 Exercise on Derived Functors -- A3.10 Tor -- A3.10.1 Exercises: Tor -- A3.1l Ext -- A3.11.1
Exercises: Ext -- A3.11.2 Local Cohomology -- II: From Mapping Cones to Spectral Sequences -- A3.12 The Mapping Cone and Double Complexe -- A3.12.1 Exercises: Mapping Cones and Double Complexes -- A3.13 Spectral Sequences -- A3.13.1
Mapping Cones Revisited -- A3.13.2 Exact Couples -- A3.13.3 Filtered Differential Modules and Complexes -- A3.13.4 The Spectral Sequence of a Double Complex -- A3.13.5 Exact Sequence of Terms of Low Degree -- A3.13.6 Exercises on
Spectral Sequences -- A3.14 Derived Categories -- A3.14.1 Step One: The Homotopy Category of Complexes -- A3.14.2 Step Two: The Derived Category -- A3.14.3 Exercises on the Derived Category -- Appendix 4 A Sketch of Local Cohomology --
A4.1 Local Cohomology and Global Cohomology -- A4.2 Local Duality -- A4.3 Depth and Dimensio -- Appendix 5 Category Theory -- A5.1 Categories, Functors, and Natural Transformations -- A5.2 Adjoint Functors -- A5.2.1 Uniqueness --
A5.2.2 Some Examples -- A5.2.3 Another Characterization of Adjoints -- A5.2.4 Adjoints and Limits -- A5.3 Representable Functors and Yoneda's Lemma -- Appendix 6 Limits and Colimits -- A6.1 Colimits in the Category of Modules -- A6.2
Flat Modules as Colimits of Free Modules -- A6.3 Colimits in the Category of Commutative Algebras -- A6.4 Exercises -- Appendix 7 Where Next? -- References -- Index of Notation
ISBN:9781461253501
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Graduate Texts in Mathematics: 150
Keywords: Mathematics , Algebraic geometry , Mathematics , Algebraic Geometry
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Call number:SPRINGER-1994-9789401715560:ONLINE Show nearby items on shelf
Title:Finite Dimensional Algebras and Related Topics
Author(s):
Date:1994
Size:1 online resource (392 p.)
Note:10.1007/978-94-017-1556-0
Contents:Equivalences of Blocks of Group Algebras -- On the Endomorphism Algebras of Gelfand-Graev Representations -- Harish-Chandra Vertices, Green Correspondence in Hecke Algebras, and Steinbergs Tensor Product Theorem in Nondescribing
Characteristic -- On Tilting Modules and Invariants for Algebraic Groups -- Harish-Chandra Subalgebras and Gelfand-Zetlin Modules -- Algebras Associated to Bruhat Intervals and Polyhedral Cones -- Symmetric Groups and Quasi-Hereditary
Algebras -- Quasitilted Algebras -- Tilting Theory and Differential Graded Algebras -- Wild Canonical Algebras and Rings of Automorphic Forms -- The Ext Algebra of a Highest Weight Category -- Coxeter transformations and the
representation theory of algebras -- Translation Functors and Equivalences of Derived Categories for Blocks of Algebraic Groups -- Blocks with cyclic defect (Green orders) -- Rigid and Exceptional Sheaves on a Del Pezzo Surface --
Quasihereditary algebras and Kazhdan-Lusztig theory -- Cycles in Module Categories -- Relative Homology -- Tilting Theory and Selfinjective Algebras
ISBN:9789401715560
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:NATO ASI Series, Series C: Mathematical and Physical Sciences: 424
Keywords: Mathematics , Algebra , Commutative algebra , Commutative rings , Nonassociative rings , Rings (Algebra) , Mathematics , Non-associative Rings and Algebras , Commutative Rings and Algebras , Algebra
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Call number:SPRINGER-1994-9780817647711:ONLINE Show nearby items on shelf
Title:Discriminants, Resultants, and Multidimensional Determinants
Author(s): Israel M Gelfand
Date:1994
Size:1 online resource (523 p.)
Note:10.1007/978-0-8176-4771-1
Contents:General Discriminants and Resultants -- Projective Dual Varieties and General Discriminants -- The Cayley Method for Studying Discriminants -- Associated Varieties and General Resultants -- Chow Varieties -- A-Discriminants and
A-Resultants -- Toric Varieties -- Newton Polytopes and Chow Polytopes -- Triangulations and Secondary Polytopes -- A-Resultants and Chow Polytopes of Toric Varieties -- A-Discriminants -- Principal A-Determinants -- Regular
A-Determinants and A-Discriminants -- Classical Discriminants and Resultants -- Discriminants and Resultants for Polynomials in One Variable -- Discriminants and Resultants for Forms in Several Variables -- Hyperdeterminants
ISBN:9780817647711
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Algebra , Algebraic geometry , Commutative algebra , Commutative rings , Matrix theory , Mathematics , Algebra , General Algebraic Systems , Commutative Rings and Algebras , Linear and Multilinear Algebras, Matrix Theory , Algebraic Geometry
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Call number:SPRINGER-1993-9789401709385:ONLINE Show nearby items on shelf
Title:Boolean Constructions in Universal Algebras
Author(s): A. G Pinus
Date:1993
Size:1 online resource (352 p.)
Note:10.1007/978-94-017-0938-5
Contents:1. Introduction -- 2. Boolean Constructions in Universal Algebras -- 3. Varieties: Spectra, Skeletons, Categories -- 13. Elementary Theories of Congruence-Distributive Variety Skeletons -- 14. Some Theorems on Boolean Algebras -- 15.
On Better Quasi-Orders -- References
ISBN:9789401709385
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Mathematics and Its Applications : 242
Keywords: Mathematics , Commutative algebra , Commutative rings , System theory , Mathematical logic , Mathematics , Mathematical Logic and Foundations , Commutative Rings and Algebras , Systems Theory, Control
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Call number:SPRINGER-1993-9789401708395:ONLINE Show nearby items on shelf
Title:Basic Structures of Modern Algebra
Author(s): Yuri Bahturin
Date:1993
Size:1 online resource (422 p.)
Note:10.1007/978-94-017-0839-5
Contents:1. Commutative algebra -- 2. Groups -- 3. Associative rings -- 4. Lie algebras -- 5. Homological algebra -- 6. Algebraic groups -- 7. Varieties of algebras -- Set-theoretic supplement -- References -- Symbol index
ISBN:9789401708395
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Mathematics and Its Applications : 265
Keywords: Mathematics , Associative rings , Rings (Algebra) , Commutative algebra , Commutative rings , Group theory , Nonassociative rings , Mathematics , Commutative Rings and Algebras , Associative Rings and Algebras , Non-associative Rings and Algebras , Group Theory and Generalizations
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Call number:SPRINGER-1993-9781461209133:ONLINE Show nearby items on shelf
Title:Gröbner Bases A Computational Approach to Commutative Algebra
Author(s): Thomas Becker
Date:1993
Size:1 online resource (576 p.)
Note:10.1007/978-1-4612-0913-3
Contents:0 Basics -- 0.1 Natural Numbers and Integers -- 0.2 Maps -- 0.3 Mathematical Algorithms -- Notes -- 1 Commutative Rings with Unity -- 1.1 Why Abstract Algebra? -- 1.2 Groups -- 1.3 Rings -- 1.4 Subrings and Homomorphisms -- 1.5 Ideals
and Residue Class Rings -- 1.6 The Homomorphism Theorem -- 1.7 Gcd’s, Lcm’s, and Principal Ideal Domains -- 1.8 Maximal and Prime Ideals -- 1.9 Prime Rings and Characteristic -- 1.10 Adjunction, Products, and Quotient Rings -- Notes --
2 Polynomial Rings -- 2.1 Definitions -- 2.2 Euclidean Domains -- 2.3 Unique Factorization Domains -- 2.4 The Gaussian Lemma -- 2.5 Polynomial Gcd’s -- 2.6 Squarefree Decomposition of Polynomials -- 2.7 Factorization of Polynomials --
2.8 The Chinese Remainder Theorem -- Notes -- 3 Vector Spaces and Modules -- 3.1 Vector Spaces -- 3.2 Independent Sets and Dimension -- 3.3 Modules -- Notes -- 4 Orders and Abstract Reduction Relations -- 4.1 The Axiom of Choice and
Some Consequences in Algebra -- 4.2 Relations -- 4.3 Foundedness Properties -- 4.4 Some Special Orders -- 4.5 Reduction Relations -- 4.6 Computing in Algebraic Structures -- Notes -- 5 Gröbner Bases -- 5.1 Term Orders and Polynomial
Reductions -- 5.2 Gröbner Bases—Existence and Uniqueness -- 5.3 Gröbner Bases—Construction -- 5.4 Standard Representations -- 5.5 Improved Gröbner Basis Algorithms -- 5.6 The Extended Gröbner Basis Algorithm -- Notes -- 6 First
Applications of Gröbner Bases -- 6.1 Computation of Syzygies -- 6.2 Basic Algorithms in Ideal Theory -- 6.3 Dimension of Ideals -- 6.4 Uniform Word Problems -- Notes -- 7 Field Extensions and the Hilbert Nullstellensatz -- 7.1 Field
Extensions -- 7.2 The Algebraic Closure of a Field -- 7.3 Separable Polynomials and Perfect Fields -- 7.4 The Hilbert Nullstellensatz -- 7.5 Height and Depth of Prime Ideals -- 7.6 Implicitization of Rational Parametrizations -- 7.7
Invertibility of Polynomial Maps -- Notes -- 8 Decomposition, Radical, and Zeroes of Ideals -- 8.1 Preliminaries -- 8.2 The Radical of a Zero-Dimensional Ideal -- 8.3 The Number of Zeroes of an Ideal -- 8.4 Primary Ideals -- 8.5
Primary Decomposition in Noetherian Rings -- 8.6 Primary Decomposition of Zero-Dimensional Ideals -- 8.7 Radical and Decomposition in Higher Dimensions -- 8.8 Computing Real Zeroes of Polynomial Systems -- Notes -- 9 Linear Algebra in
Residue Class Rings -- 9.1 Gröbner Bases and Reduced Terms -- 9.2 Computing in Finitely Generated Algebras -- 9.3 Dimensions and the Hilbert Function -- Notes -- 10 Variations on Gröbner Bases -- 10.1 Gröbner Bases over PID’s and
Euclidean Domains -- 10.2 Homogeneous Gröbner Bases -- 10.3 Homogenization -- 10.4 Gröbner Bases for Polynomial Modules -- 10.5 Systems of Linear Equations -- 10.6 Standard Bases and the Tangent Cone -- 10.7 Symmetric Functions --
Notes -- Appendix: Outlook on Advanced and Related Topics -- Complexity of Gröbner Basis Constructions -- Term Orders and Universal Gröbner Bases -- Comprehensive Gröbner Bases -- Gröbner Bases and Automatic Theorem Proving --
Characteristic Sets and Wu-Ritt Reduction -- Term Rewriting -- Standard Bases in Power Series Rings -- Non-Commutative Gröbner Bases -- Gröbner Bases and Differential Algebra -- Selected Bibliography -- Conference Proceedings -- Books
and Monographs -- Articles -- List of Symbols
ISBN:9781461209133
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Graduate Texts in Mathematics: 141
Keywords: Mathematics , Algebra , Group theory , Mathematics , Group Theory and Generalizations , Algebra
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Call number:SPRINGER-1993-9781461208891:ONLINE Show nearby items on shelf
Title:Noncommutative Algebra
Author(s): Benson Farb
Date:1993
Size:1 online resource (226 p.)
Note:10.1007/978-1-4612-0889-1
Contents:I The Core Course -- 0 Background Material -- 1 Semisimple Modules & Rings and the Wedderburn Structure Theorem -- 2 The Jacobson Radical -- 3 Central Simple Algebras -- 4 The Brauer Group -- II Selected Topics -- 5 Primitive Rings
and the Density Theorem -- 6 Burnside’s Theorem and Representations of Finite Groups -- 7 The Global Dimension of a Ring -- 8 The Brauer Group of a Commutative Ring -- III Supplementary Exercises -- References
ISBN:9781461208891
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Graduate Texts in Mathematics: 144
Keywords: Mathematics , Algebra , Mathematics , Algebra
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Call number:SPRINGER-1992-9789401127165:ONLINE Show nearby items on shelf
Title:Approximation Theorems in Commutative Algebra Classical and Categorical Methods
Author(s): J Alajbegović
Date:1992
Size:1 online resource (330 p.)
Note:10.1007/978-94-011-2716-5
Contents:I Classical Methods -- 1 Approximation Theorems For Valuations On Fields -- 2 Valuations On Commutative Rings -- 3 Ordered Groups And Homomorphisms -- 4 Approximation Theorems For Multi-Structures -- II Categorical Methods -- 5
Categorical Logic -- 6 Approximation Theorems In Categories -- Index of Notation
ISBN:9789401127165
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Mathematics and Its Applications(East European Series): 59
Keywords: Mathematics , Category theory (Mathematics) , Homological algebra , Commutative algebra , Commutative rings , Algebra , Ordered algebraic structures , Mathematics , Commutative Rings and Algebras , Category Theory, Homological Algebra , Order, Lattices, Ordered Algebraic Structures
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Call number:SPRINGER-1991-9789401136044:ONLINE Show nearby items on shelf
Title:Automorphisms and Derivations of Associative Rings
Author(s): V. K Kharchenko
Date:1991
Size:1 online resource (385 p.)
Note:10.1007/978-94-011-3604-4
Contents:1. Structure of Rings -- 1.1 Baer Radical and Semiprimeness -- 1.2 Automorphism Groups and Lie Differential Algebras -- 1.3 Bergman-Isaacs Theorem. Shelter Integrality -- 1.4 Martindale Ring of Quotients -- 1.5 The Generalized
Centroid of a Semiprime Ring -- 1.6 Modules over a Generalized Centroid -- 1.7 Extension of Automorphisms to a Ring of Quotients. Conjugation Modules -- 1.8 Extension of Derivations to a Ring of Quotients -- 1.9 The Canonical Sheaf of
a Semiprime Ring -- 1.10 Invariant Sheaves -- 1.11 The Metatheorem -- 1.12 Stalks of Canonical and Invariant Sheaves -- 1.13 Martindale’s Theorem -- 1.14 Quite Primitive Rings -- 1.15 Rings of Quotients of Quite Primitive Rings -- 2.
On Algebraic Independence of Automorphisms And Derivations -- 2.0 Trivial Algebraic Dependences -- 2.1 The Process of Reducing Polynomials -- 2.2 Linear Differential Identities with Automorphisms -- 2.3 Multilinear Differential
Identities with Automorphisms -- 2.4 Differential Identities of Prime Rings -- 2.5 Differential Identities of Semiprime Rings -- 2.6 Essential Identities -- 2.7 Some Applications: Galois Extentions of Pi-Rings Algebraic Automorphisms
and Derivations Associative Envelopes of Lie-Algebras of Derivations -- 3. The Galois Theory of Prime Rings (The Case Of Automorphisms) -- 3.1 Basic Notions -- 3.2 Some Properties of Finite Groups of Outer Automorphisms -- 3.3
Centralizers of Finite-Dimensional Algebras -- 3.4 Trace Forms -- 3.5 Galois Groups -- 3.6 Maschke Groups. Prime Dimensions -- 3.7 Bimodule Properties of Fixed Rings -- 3.8 Ring of Quotients of a Fixed Ring -- 3.9 Galois Subrings for
M-Groups -- 3.10 Correspondence Theorems -- 3.11 Extension of Isomorphisms -- 4. The Galois Theory of Prime Rings (The Case Of Derivations) -- 4.1 Duality for Derivations in the Multiplication Algebra -- 4.2 Transformation of
Differential Forms -- 4.3 Universal Constants -- 4.4 Shirshov Finiteness -- 4.5 The Correspondence Theorem -- 4.6 Extension of Derivations -- 5. The Galois Theory of Semiprime Rings -- 5.1 Essential Trace Forms -- 5.2 Intermediate
Subrings -- 5.3 The Correspondence Theorem for Derivations -- 5.4 Basic Notions of the Galois Theory of Semiprime Rings (the case of automorphisms) -- 5.5 Stalks of an Invariant Sheaf for a Regular Group. Homogenous Idempotents -- 5.6
Principal Trace Forms -- 5.7 Galois Groups -- 5.8 Galois Subrings for Regular Closed Groups -- 5.9 Correspondence and Extension Theorems -- 5.10 Shirshov Finiteness. The Structure of Bimodules -- 6. Applications -- 6.1 Free Algebras --
6.2 Noncommutative Invariants -- 6.3 Relations of a Ring with Fixed Rings -- 6.4 Relations of a Semiprime Ring with Ring of Constants -- 6.5 Hopf Algebras -- References
ISBN:9789401136044
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Mathematics and Its Applications (Soviet Series): 69
Keywords: Mathematics , Associative rings , Rings (Algebra) , Commutative algebra , Commutative rings , Nonassociative rings , Mathematics , Commutative Rings and Algebras , Associative Rings and Algebras , Non-associative Rings and Algebras
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Call number:SPRINGER-1991-9781461204411:ONLINE Show nearby items on shelf
Title:Effective Methods in Algebraic Geometry
Author(s):
Date:1991
Size:1 online resource (502 p.)
Note:10.1007/978-1-4612-0441-1
Contents:On Lack of Effectiveness in Semi-algebraic Geometry -- A simple constructive proof of Canonical Resolution of Singularities -- Local Membership Problems for Polynomial Ideals -- Un Algorithme pour le Calcul des Résultants -- On
algorithms for real algebraic plane curves -- Duality methods for the membership problem -- Exemples d’ensembles de Points en Position Uniforme -- Efficient Algorithms and Bounds for Wu-Ritt Characteristic Sets -- Noetherian Properties
and Growth of some Associative Algebras -- Codes and Elliptic Curves -- Algorithmes – disons rapides – pour la décomposition d’une variété algébrique en composantes irréductibles et équidimensionnelles -- Complexity of Solving Systems
of Linear Equations over the Rings of Differential Operators -- Membership problem, Representation problem and the Computation of the Radical for one-dimensional Ideals -- On the Complexity of Zero-dimensional Algebraic Systems -- A
Single Exponential Bound on the Complexity of Computing Gröbner Bases of Zero Dimensional Ideals -- Algorithms for a Multiple Algebraic Extension -- Elementary constructive theory of ordered fields -- Effective real Nullstellensatz and
variants -- Algorithms for the Solution of Systems of Linear Equations in Commutative Rings -- Une conjecture sur les anneaux de Chow A(G, ?) renforcée par un calcul formel -- Construction de courbes de genre 2 à partir de leurs
modules -- Computing Syzygies à la Gau?-Jordan -- The non-scalar Model of Complexity in Computational Geometry -- Géométrie et Interpretations Génériques, un Algorithme -- Canonical Bases: Relations with Standard Bases, Finiteness
Conditions and Application to Tame Automorphisms -- The tangent cone algorithm and some applications to local algebraic geometry -- Effective Methods for Systems of Algebraic Partial Differential Equations -- Finding roots of equations
involving functions defined by first order algebraic differential equations -- Some Effective Methods in the Openness of Loci for Cohen-Macaulay and Gorenstein Properties -- Sign determination on zero dimensional sets -- A
Classification of Finite-dimensional Monomial Algebras -- An algorithm related to compactifications of adjoint groups -- Deciding Consistency of Systems of Polynomial in Exponent Inequalities in Subexponential Time
ISBN:9781461204411
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Progress in Mathematics : 94
Keywords: Mathematics , Algebraic geometry , Mathematics , Algebraic Geometry
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Call number:SPRINGER-1989-9783662131527:ONLINE Show nearby items on shelf
Title:The Classical Groups and K-Theory
Author(s): Alexander J Hahn
Date:1989
Size:1 online resource (578 p.)
Note:10.1007/978-3-662-13152-7
Contents:Notation and Conventions -- 1. General Linear Groups, Steinberg Groups, and K-Groups -- 2. Linear Groups over Division Rings -- 3. Isomorphism Theory for the Linear Groups -- 4. Linear Groups over General Classes of Rings -- 5.
Unitary Groups, Unitary Steinberg Groups, and Unitary K-Groups -- 6. Unitary Groups over Division Rings -- 7. Clifford Algebras and Orthogonal Groups over Commutative Rings -- 8. Isomorphism Theory for the Unitary Groups -- 9. Unitary
Groups over General Classes of Form Rings -- Concluding Remarks -- Index of Concepts -- Index of Symbols
ISBN:9783662131527
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics: 291
Keywords: Mathematics , Group theory , Number theory , Topology , Mathematics , Group Theory and Generalizations , Number Theory , Topology
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Call number:SPRINGER-1989-9783540461593:ONLINE Show nearby items on shelf
Title:Commutative Coherent Rings
Author(s): Sarah Glaz
Date:1989
Size:1 online resource (347 p.)
Note:10.1007/BFb0084570
Contents:Preliminaries -- to coherence -- Fundamental concepts -- Ring extensions -- Ring constructions and overrings -- Particular coherent rings -- Polynomial rings -- Coherent algebras
ISBN:9783540461593
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Lecture Notes in Mathematics: 1371
Keywords: Mathematics , K-theory , Mathematics , K-Theory
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Call number:SPRINGER-1989-9781461236948:ONLINE Show nearby items on shelf
Title:Nathan Jacobson Collected Mathematical Papers Volume 2 (1947–1965)
Author(s): Nathan Jacobson
Date:1989
Size:1 online resource (556 p.)
Note:10.1007/978-1-4612-3694-8
Contents:Personal History and Commentary (1947–1955) -- Research Papers, 1947–1955 -- [39] Lie and Jordan triple systems -- [40] Classification and representation of semi-simple Jordan algebras (with F. D. Jacobson) -- [41] Derivation algebras
and multiplication algebras of semi-simple Jordan algebras -- [42] Enveloping algebras of semi-simple Lie algebras -- [43] Some remarks on one-sided inverses -- [44] Jordan homomorphisms of rings (with C. E. Rickart) -- [45] Completely
reducible Lie algebras of linear transformations -- [46] General representation theory of Jordan algebras -- [47] Une généralisation du théorème d’Engel -- [48] Homomorphisms of Jordan rings of self-adjoint elements (with C. E.
Rickart) -- [49] A note on Lie algebras of characteristic p -- [50] Operator commutativity in Jordan algebras -- [51] A Kronecker factorization theorem for Cayley algebras and the exceptional simple Jordan algebra -- [52] Structure of
alternative and Jordan bimodules -- [53] A note on automorphisms and derivations of Lie algebras -- [54] Commutative restricted Lie algebras -- [55] A note on two dimensional division ring extensions -- Personal History and Commentary
(1956–1965) -- Research Papers, 1956–1965 -- [56] A theorem on the structure of Jordan algebras -- [57] Generation of separable and central simple algebras -- [58] On reduced exceptional simple Jordan algebras (with A. A. Albert) --
[59] On Jordan algebras with two generators (with L. J. Paige) -- [60] Composition algebras and their automorphisms -- [61] Nilpotent elements in semi-simple Jordan algebras -- [62] A note on three dimensional simple Lie algebras --
[63] Some groups of transformations defined by Jordan algebras I -- [64] Some groups of transformations defined by Jordan algebras II -- [65] Some groups of transformations defined by Jordan algebras III -- [66] MacDonald’s theorem on
Jordan algebras -- [67] A coordinatization theorem for Jordan algebras -- [68] A note on automorphisms of Lie algebras -- [69] Generic norm of an algebra -- [70] Clifford algebras for algebras with involution of type D -- [71] Triality
and Lie algebras of type D4 -- Permissions
ISBN:9781461236948
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Science , Science, general , Science, general
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Call number:SPRINGER-1989-9781461236603:ONLINE Show nearby items on shelf
Title:Commutative Algebra Proceedings of a Microprogram Held June 15–July 2, 1987
Author(s):
Date:1989
Size:1 online resource (3 p.)
Note:10.1007/978-1-4612-3660-3
Contents:Representations, Resolutions and Intertwining Numbers -- Cohen-Macaulay Modules for Graded Cohen-Macaulay Rings and Their Completions -- Homological Asymptotics of Modules Over Local Rings -- On Ulrich-Modules Over Hypersurface Rings
-- Differential Structure of Étale Extensions of Polynomial Algebras -- Additions to the Theory of Algebras with Straightening Law -- Syzygies and Homological Conjectures -- Remarks on Points in a Projective Space -- Rank Varieties of
Matrices -- Order Ideals -- A Characterization of F-Regularity in Terms of F-Purity -- Surface Singularities of Finite Buchsbaum-Representation Type -- Some Transcendence Degree Questions -- Exceptional Prime Divisors Of
Two-Dimensional Local Domains -- Tight Closure -- Complete Ideals in Two-Dimensional Regular Local Rings -- Powers Of Licci Ideals -- The Hilbert Function of a Gorenstein Artin Algebra -- On Unramifying Transcendence Base -- A Survey
of Problems and Results on the Number of Defining Equations -- Integrally Closed Projectively Equivalent Ideals -- Izumi’s Theorem -- Intersection Theorems -- One-Fibered Ideals -- A Method for the Study of Artinian Modules, With an
Application to Asymptotic Behavior -- Symmetric Algebras and Factoriality -- Noetherian Rings of Bounded Representation Type
ISBN:9781461236603
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Mathematical Sciences Research Institute Publications: 15
Keywords: Mathematics , Algebra , Mathematics , Algebra
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Call number:SPRINGER-1988-9783540459941:ONLINE Show nearby items on shelf
Title:Algebra Some Current Trends Proceedings of the 5th National School in Algebra held in Varna, Bulgaria, Sept. 24 – Oct. 4, 1986
Author(s):
Date:1988
Size:1 online resource (248 p.)
Note:10.1007/BFb0082013
Contents:Matrix factorizations of homogeneous polynomials -- Some new results in the combinatorial theory of rings and groups -- On representations of infinite groups -- Integral manifolds, harmonic mappings, and the abelian subspace problem
-- Valuations on ree fields -- Standard bases and homology -- Semisimple superalgebras -- On the laws of finite dimensional representations of solvable lie algebras and groups -- Lie groups and ergodic theory -- Galois theory of
databases -- On the codimensions of matrix algebras -- Homology of free loop spaces, cyclic homology and non-rational poincare-betti series in commutative algebra -- Incomplete sums and two applications of Deligne's result --
Eigenvalues of matrices of complex representations of finite groups of lie type -- Normal fitting classes of groups and generalizations -- On the nilpotency of nil algebras
ISBN:9783540459941
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Lecture Notes in Mathematics: 1352
Keywords: Mathematics , Algebra , Mathematics , Mathematics , Algebra , Mathematics Education
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Call number:SPRINGER-1988-9783540392781:ONLINE Show nearby items on shelf
Title:Ring Theory Proceedings of a Conference held in Granada, Spain, Sept. 1–6, 1986
Author(s):
Date:1988
Size:1 online resource (336 p.)
Note:10.1007/BFb0100908
Contents:Stable range of aleph-nought-continuou regular rings -- On filtered rings with noetherian associated graded rings -- Duality theorems for group actions and gradings -- Chain rings and valuations -- Directly finite ?0-complete regular
rings are unit-regular -- Cancellation theorems for projective graded modules -- Centraliseurs dans les anneaux de polynomes differentiels formels et leurs corps de fractions -- Regular group algebras whose maximal right and left
quotient rings coincide -- A survey of recent work on the cohomology of one-relator associative algebras -- Semiprime alternative rings with A.C.C. -- Continuous and pf rings of quotients -- Rings of quotients of endomorphism rings --
Some criteria for solvability of systems of linear equations over modules -- Centers of generic division algebras and zeta - functions -- Frobenius reciprocity and G0 of skew group rings -- Algèbre homologique et opérateurs
différentiels -- Cancellation modules over regular rings -- Noetherian property for semigroup rings -- Semi-rings and spectral spaces -- Some new progress on the isomorphismproblem for integral group rings -- A proof of the class sum
correspondence using the real group algebra -- Une caracterisation des anneaux artiniens a ideaux principaux -- Krull and Gabriel dimension relative to a linear topology -- On determinantal ideals over certain non commutative rings --
Large subdirect products -- Socle and semicocritical series -- Local cohomology of noncommutative rings: a geometric interpretation
ISBN:9783540392781
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Lecture Notes in Mathematics: 1328
Keywords: Mathematics , Algebra , Mathematics , Algebra
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Call number:SPRINGER-1988-9781461239444:ONLINE Show nearby items on shelf
Title:Graded Orders
Author(s): L. le Bruyn
Date:1988
Size:1 online resource (208 p.)
Note:10.1007/978-1-4612-3944-4
Contents:I. Commutative Arithmetical Graded Rings -- I.1. Graded Krull Domains -- I.2. Valuations and the structure of Gr-Dedekind Rings -- II. Graded Rings and Orders -- II.1. Graded Rings over Goldie Rings -- II.2. Divisorially Graded Rings
and Generalized Rees Rings -- II.3. Graded Rings Satisfying Polynomial Identities -- II.4. Orders and Graded Orders -- II.5. Some General Techniques -- III. Arithmetically Graded Rings over Orders -- III.1. Orders Graded by Torsion
Free Abelian Groups -- III.2. Orders Graded by Finite Groups -- III.3. Generalized Crossed Product Azumaya Algebras -- III.4. Extensions of Tame Orders and Related Sequences -- IV. Regular Orders -- IV.1. Moderated Gorenstein and
Regular Orders -- IV.2. Orders of Finite Representation Type -- IV.3. Regularizable Domains -- IV.4. Smooth Tame Orders -- IV.5. Weak Brauer-Severi Schemes -- V. Two Dimensional Tame and Maximal Orders of Finite Representation Type --
V.1. Introduction -- V.2. Rational Double Points Associated to Two-dimensional Tame Orders of Finite Representation Type -- V.3. Skew Group Rings and Projective Representations Associated to Two-dimensional Tame Orders of Finite
Representation Type -- V.4. Classification of Two-dimensional Maximal Orders of Finite Representation Type -- V.5. Appendix: Recent Work of I. Reiten and the Second Author -- References
ISBN:9781461239444
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Keywords: Mathematics , Algebra , Ordered algebraic structures , Mathematics , Order, Lattices, Ordered Algebraic Structures
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Call number:SPRINGER-1988-9781441986405:ONLINE Show nearby items on shelf
Title:A Course in Constructive Algebra
Author(s): Ray Mines
Date:1988
Size:1 online resource (344 p.)
Note:10.1007/978-1-4419-8640-5
Contents:I. Sets -- 1. Constructive vs. classical mathematics -- 2. Sets, subsets and functions -- 3. Choice -- 4. Categories -- 5. Partially ordered sets and lattices -- 6. Well-founded sets and ordinals -- II. Basic Algebra -- 1. Groups --
2. Rings and fields -- 3. Real numbers -- 4. Modules -- 5. Polynomial rings -- 6. Matrices and vector spaces -- 7. Determinants -- 8. Symmetric polynomials -- III. Rings And Modules -- 1. Quasi-regular ideals -- 2. Coherent and
Noetherian modules -- 3. Localization -- 4. Tensor products -- 5. Flat modules -- 6. Local rings -- 7. Commutative local rings -- IV. Divisibility in Discrete Domains -- 1. Cancellation monoids -- 2. UFD's and Bézout domains -- 3.
Dedekind-Hasse rings and Euclidean domains -- 4. Polynomial rings -- V. Principal Ideal Domains -- 1. Diagonalizing matrices -- 2. Finitely presented modules -- 3. Torsion modules, p-components, elementary divisors -- 4. Linear
transformations -- VI. Field Theory -- 1. Integral extensions and impotent rings -- 2. Algebraic independence and transcendence bases -- 3. Splitting fields and algebraic closures -- 4. Separability and diagonalizability -- 5.
Primitive elements -- 6. Separability and characteristic p -- 7. Perfect fields -- 8. Galois theory -- VII. Factoring Polynomials -- 1. Factorial and separably factorial fields -- 2. Extensions of (separably) factorial fields -- 3.
Condition p -- 4. The fundamental theorem of algebra -- VIII. Commutative Noetherian Rings -- 1. The Hilbert basis theorem -- 2. Noether normalization and the Artin-Rees lemma -- 3. The Nullstellensatz -- 4. Tennenbaum' s approach to
the Hilbert basis theorem -- 5. Primary ideals -- 6. Localization -- 7. Primary decomposition -- 8. Lasker-Noether rings -- 9. Fully Lasker-Noether rings -- 10. The principal ideal theorem -- IX. Finite Dimensional Algebras -- 1.
Representations -- 2. The density theorem -- 3. The radical and summands -- 4. Wedderburn's theorem, part one -- 5. Matrix rings and division algebras -- X. Free Groups -- 1. Existence and uniqueness -- 2. Nielsen sets -- 3. Finitely
generated subgroups -- 4. Detachable subgroups of finite-rank free groups -- 5. Conjugate subgroups -- XI. Abelian Groups -- 1. Finite-rank torsion-free groups -- 2. Divisible groups -- 3. Height functions on p-groups -- 4. Ulm's
theorem -- 5. Construction of Ulm groups -- XII. Valuation Theory -- 1. Valuations -- 2. Locally precompact valuations -- 3. Pseudofactorial fields -- 4. Normed vector spaces -- 5. Real and complex fields -- 6. Hensel's lemma -- 7.
Extensions of valuations -- 8. e and f -- XIII. Dedekind Domains -- 1. Dedekind sets of valuations -- 2. Ideal theory -- 3. Finite extensions
ISBN:9781441986405
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Keywords: Mathematics , Algebra , Mathematics , Algebra
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Call number:SPRINGER-1987-9789400938359:ONLINE Show nearby items on shelf
Title:Dimensions of Ring Theory
Author(s): Constantin Nǎstǎsescu
Date:1987
Size:1 online resource (360 p.)
Note:10.1007/978-94-009-3835-9
Contents:1. Finiteness Conditions for Lattices -- 1.1. Lattices -- 1.2. Noetherian and Artinian Lattices -- 1.3. Lattices of Finite Length -- 1.4. Irreducible Elements in a Lattice -- 1.5. Goldie Dimension of a Modular Lattice -- 1.6. Goldie
Dimension and Chain Conditions for Modular Lattices with Finite Group Actions -- 1.7. Complements and Pseudo-Complements -- 1.8. Semiatomic Lattices and Compactly Generated Lattices -- 1.9. Semiartinian Lattices -- 1.10. Indecomposable
Elements in a Lattice -- 1.11. Exercises -- Bibliographical Comments to Chapter 1 -- 2. Finiteness Conditions for Modules -- 2.1. Modules -- 2.2. The Lattice of Submodules of a Module -- 2.3. Noetherian and Artinian Modules -- 2.4.
Modules of Finite Length -- 2.5. Semisimple Modules -- 2.6. Semisimple and Simple Artinian Rings -- 2.7. The Jacobson Radical and the Prime Radical of a Ring -- 2.8. Rings of Fractions. Goldie’s Theorems -- 2.9. Artinian Modules which
are Noetherian -- 2.10. Projective and Infective Modules -- 2.11. Tensor Product and Flat Modules -- 2.12. Normalizing Extensions of a Ring -- 2.13. Graded Rings and Modules -- 2.14. Graded Rings and Modules of Type ?. Internal
Homogenisation -- 2.15. Noetherian Modules over Graded Rings of Type ?. Applications -- 2.16. Strongly Graded Rings and Clifford Systems for Finite Groups -- 2.17. Invariants of a Finite Group Action -- 2.18. Exercises --
Bibliographical Comments to Chapter 2 -- 3. Krull Dimension and Gabriel Dimension of an Ordered Set -- 3.1. Definitions and Basic Properties -- 3.2. The Krull Dimension of a Modular Lattice -- 3.3. Critical Composition Series of a
Lattice -- 3.4. The Gabriel Dimension of a Modular Lattice -- 3.5. Comparison of Krull and Gabriel Dimension -- 3.6. Exercises -- Bibliographical Comments to Chapter 3 -- 4. Krull Dimension and Gabriel Dimension of Rings and Modules --
4.1. Definitions and Generalities -- 4.2. Krull and Gabriel Dimension of Some Special Classes of Rings and Modules -- 4.3. Exercises -- Bibliographical Comments to Chapter 4 -- 5. Rings with Krull Dimension -- 5.1. Nil Ideals -- 5.2.
Semiprime Rings with Krull Dimension -- 5.3. Classical Krull Dimension of a Ring -- 5.4. Associated prime Ideals -- 5.5. Fully Left Bounded Rings with Krull Dimension -- 5.6. Examples of Noetherian Rings of Arbitrary Krull Dimension --
5.7. Exercises -- Bibliographical Comments to Chapter 5 -- 6. Krull Dimension of Noetherian Rings. The Principal Ideal Theorem -- 6.1. Fully Left Bounded Left Noetherian Rings -- 6.2. The Reduced Rank of a Module -- 6.3. Noetherian
Rings Satisfying Condition H -- 6.4. Fully Bounded Noetherian Rings -- 6.5. Krull Dimension and Invertible Ideals in a Noetherian Ring -- 6.6. The Principal Ideal Theorem -- 6.7. Exercises -- Bibliographical Comments to Chapter 6 -- 7.
Relative Krull and Gabriel Dimensions -- 7.1. Additive Topologies and Torsion Theories -- 7.2. The Lattices CF (M) and CHg -- 7.3. Relative Krull Dimension -- 7.4. Relative Krull Dimension Applied to the Principal Ideal Theorem -- 7.5.
Relative Gabriel Dimension -- 7.6. Relative Krull and Gabriel Dimensions of Graded Rings -- 7.7. Exercises -- Bibliographical Comments to Chapter 7 -- 8. Homological Dimensions -- 8.1. The Projective Dimension of a Module -- 8.2.
Homological Dimension of Polynomial Rings and Rings of Formal Power Series -- 8.3. Injective Dimension of a Module -- 8.4. The Flat Dimension of a Module -- 8.5. The Artin-Rees Property and Homological Dimensions -- 8.6. Regular Local
Rings -- 8.7. Exercises -- Bibliographical Comments to Chapter 8 -- 9. Rings of Finite Global Dimension -- 9.1. The Zariski Topology -- 9.2. The Local Study of Homological Dimension -- 9.3. Rings Integral over their Centres -- 9.4.
Commutative Rings of Finite Global Dimension -- 9.5. Exercises -- Bibliographical Comments to Chapter 9 -- 10. The Gelfand-Kirillov Dimension -- 10.1. Definitions and Basic Properties -- 10.2. GK-dimension of Filtered and Graded
Algebras -- 10.3. Applications to Special Classes of Rings -- 10.4. Exercises -- Bibliographical Comments to Chapter 10 -- References
ISBN:9789400938359
Series:eBooks
Series:SpringerLink (Online service)
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Series:Mathematics and Its Applications : 36
Keywords: Mathematics , Associative rings , Rings (Algebra) , Commutative algebra , Commutative rings , Nonassociative rings , Mathematics , Commutative Rings and Algebras , Associative Rings and Algebras , Non-associative Rings and Algebras
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Call number:SPRINGER-1986-9783540398332:ONLINE Show nearby items on shelf
Title:Ring Theory Proceedings of an International Conference held in Antwerp, April 1–5, 1985
Author(s):
Date:1986
Size:1 online resource (236 p.)
Note:10.1007/BFb0076306
Contents:Action de groupes sur A1(?) -- Conditions Noethériennes dans les anneaux gradués -- The subgroup structure of the brauer group of RG-dimodule algebras -- A graded version of artin's refinement theorem -- Exemples de sous-corps
commutatifs maximaux dans D2(k) -- Semigroup rings which are separable algebras -- Classnumbers of maximal orders in central simple algebras over global function fields -- Generating the ring of matrix invariants -- Hereditary and
semihereditary endomorphism rings -- The poincare series of ? m,2 -- An explicit description of ?3,2 -- S-dérivations algébriques sur les anneaux premiers -- On affine algebras -- Ideaux premiers purement codimensionels d'algebres
enveloppantes -- Sur le groupe des extensions cubiques -- Universal localisation for hereditary rings and quivers -- Differential operators on commutative algebras -- Height relative to a torsion theory -- Polynomes tordus et T-anneaux
a gauche -- The algebraic index of a division algebra -- Hecke Actions on Relative Picard Groups -- The general linear group of discrete hodge algebras
ISBN:9783540398332
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Series:Lecture Notes in Mathematics: 1197
Keywords: Mathematics , Algebra , Mathematics , Algebra
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Call number:SPRINGER-1986-9781461575542:ONLINE Show nearby items on shelf
Title:Optimal Unbiased Estimation of Variance Components
Author(s): James D Malley
Date:1986
Size:1 online resource (146 p.)
Note:10.1007/978-1-4615-7554-2
Contents:One: The Basic Model and the Estimation Problem -- 1.1 Introduction -- 1.2 An Example -- 1.3 The Matrix Formulation -- 1.4 The Estimation Criteria -- 1.5 Properties of the Criteria -- 1.6 Selection of Estimation Criteria -- Two: Basic
Linear Technique -- 2.1 Introduction -- 2.2 The vec and mat Operators -- 2.3 Useful Properties of the Operators -- Three: Linearization of the Basic Model -- 3.1 Introduction -- 3.2 The First Linearization -- 3.3 Calculation of var(y)
-- 3.4 The Second Linearization of the Basic Model -- 3.5 Additional Details of the Linearizations -- Four: The Ordinary Least Squares Estimates -- 4.1 Introduction -- 4.2 The Ordinary Least Squares Estimates: Calculation -- 4.3 The
Inner Structure of the Linearization -- 4.4 Estimable Functions of the Components -- 4.5 Further OLS Facts -- Five: The Seely-Zyskind Results -- 5.1 Introduction -- 5.2 The General Gauss-Markov Theorem: Some History and Motivation --
5.3 The General Gauss-Markov Theorem: Preliminaries -- 5.4 The General Gauss-Markov Theorem: Statement and Proof -- 5.5 The Zyskind Version of the Gauss-Markov Theorem -- 5.6 The Seely Condition for Optimal unbiased Estimation -- Six:
The General Solution to Optimal Unbiased Estimation -- 6.1 Introduction -- 6.2 A Full Statement of the Problem -- 6.3 The Lehmann-Scheffé Result -- 6.4 The Two Types of Closure -- 6.5 The General Solution -- 6.6 An Example -- Seven:
Background from Algebra -- 7.1 Introduction -- 7.2 Groups, Rings, Fields -- 7.3 Subrings and Ideals -- 7.4 Products in Jordan Rings -- 7.5 Idempotent and Nilpotent Elements -- 7.6 The Radical of an Associative or Jordan Algebra -- 7.7
Quadratic Ideals in Jordan Algebras -- Eight: The Structure of Semisimple Associative and Jordan Algebras -- 8.1 Introduction -- 8.2 The First Structure Theorem -- 8.3 Simple Jordan Algebras -- 8.4 Simple Associative Algebras -- Nine:
The Algebraic Structure of Variance Components -- 9.1 Introduction -- 9.2 The Structure of the Space of Optimal Kernels -- 9.3 The Two Algebras Generated by Sp(?2) -- 9.4 Quadratic Ideals in Sp(?2) -- 9.5 Further Properties of the
Space of Optimal Kernels -- 9.6 The Case of Sp(?2) Commutative -- 9.7 Examples of Mixed Model Structure Calculations: The Partially Balanced Incomplete Block Designs -- Ten: Statistical Consequences of the Algebraic Structure Theory --
10.1 Introduction -- 10.2 The Jordan Decomposition of an Optimal Unbiased Estimate -- 10.3 Non-Negative Unbiased Estimation -- Concluding Remarks -- References
ISBN:9781461575542
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Series:Lecture Notes in Statistics: 39
Keywords: Mathematics , Applied mathematics , Engineering mathematics , Mathematics , Applications of Mathematics
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Call number:SPRINGER-1985-9789400954601:ONLINE Show nearby items on shelf
Title:Rings and Geometry
Author(s):
Date:1985
Size:1 online resource (568 p.)
Note:10.1007/978-94-009-5460-1
Contents:I: Non-Commutative Algebraic Geometry -- Principles of non-commutative algebraic geometry -- Applications of results on generalized polynomial identities in Desarguesian projective spaces -- II: Hjelmslev Geometries -- A topological
characterization of Hjelmslev’s classical geometries -- Finite Hjelmslev planes and Klingenberg epimorphisms -- III: Geometries over Alternative Rings -- Generalizing the Moufang plane -- Projective ring planes and their homomorphisms
-- IV: Metric Ring Geometries, Linear Groups over Rings and Coordinatization -- Topics in geometric algebra over rings -- Metric geometry over local-global commutative rings -- Linear mappings of matrix rings preserving invariants --
Kinematic algebras and their geometries -- Coordinatization of lattices -- Epilog -- The advantage of geometric concepts in mathematics -- Index of Subjects
ISBN:9789400954601
Series:eBooks
Series:SpringerLink (Online service)
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Series:NATO ASI Series, Series C: Mathematical and Physical Sciences: 160
Keywords: Mathematics , Algebra , Mathematics , Algebra
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Call number:SPRINGER-1985-9783642699719:ONLINE Show nearby items on shelf
Title:Quadratic and Hermitian Forms
Author(s): Winfried Scharlau
Date:1985
Size:1 online resource (422 p.)
Note:10.1007/978-3-642-69971-9
Contents:1. Basic Concepts -- §1. Bilinear Forms and Quadratic Forms -- § 2. Matrix Notation -- § 3. Regular Spaces and Orthogonal Decomposition -- § 4. Isotropy and Hyperbolic Spaces -- §5. Witt’s Theorem -- §6. Appendix: Symmetric Bilinear
Forms and Quadratic Forms over Rings -- 2. Quadratic Forms over Fields -- §1. Grothendieck and Witt Rings -- §2. Invariants -- § 3. Examples I (Finite Fields) -- § 4. Examples II (Ordered Fields) -- § 5. Ground Field Extension and
Transfer -- §6. The Torsion of the Witt Group -- §7. Orderings, Pfister’s Local Global Principle, and Prime Ideals of the Witt Ring -- § 8. Applications of the Method of Transfer -- § 9. Description of the Witt Ring by Generators and
Relations -- § 10. Multiplicative Forms -- §11. Quaternion Algebras -- §12. The Hasse Invariant and the Witt Invariant -- §13. The Hasse Algebra -- § 14. Classification Theorems -- §15. Examples III. Ci-fields -- §16. The u-invariant
-- 3. Quadratic Forms over Formally Real Fields -- §1. Formally Real and Ordered Fields -- §2. Real Closed Fields -- §3. Hilbert’s 17th Problem and the Real Nullstellensatz -- §4. Extension of Signatures -- §5. The Space of Orderings
of a Field -- §6. The Total Signature -- §7. A Local Global Principle for Weak Isotropy -- Appendix: Places, Valuations, and Valuation Rings -- 4. Generic Methods and Pfister Forms -- §1. Chain-p-equivalence of Pfister Forms -- § 2.
Pfister’s Theorem on the Representation of Positive Functions as Sums of Squares -- §3. Casseis’ and Pfister’s Representation Theorems -- §4. Applications: Fields of Prescribed Level. Characterization of Pfister Forms -- §5. The
Function Field of a Quadratic Form and the Main Theorem of Arason and Pfister -- §6. Generic Zeros and Generic Splitting -- §7. Knebusch’s Filtration of the Witt Ring -- 5. Rational Quadratic Forms -- § 1. Symmetric Bilinear Forms and
Quadratic Forms on Finite Abelian Groups -- §2. Gaussian Sums for Quadratic Forms on Finite Abelian Groups -- §3. The Witt Group of1 -- §4. The Witt Group of 2 -- §5. Gauss’ First Proof of the Quadratic Reciprocity Law -- §6. Quadratic
Forms over the p-adic Numbers -- §7. Hilbert’s Reciprocity Law and the Hasse-Minkowski Theorem -- §8. Calculation of Gaussian Sums -- 6. Symmetric Bilinear Forms over Dedekind Rings and Global Fields -- §1. Symmetric Bilinear Forms
over Dedekind Rings -- § 2. Symmetric Bilinear Forms over Discrete Valuation Rings -- §3. Symmetric Bilinear Forms over Polynomial Rings and Rational Function Fields -- §4. Symmetric Bilinear Forms over p-adic Fields -- § 5. The
Hilbert Reciprocity Theorem -- § 6. The Hasse-Minkowski Theorem -- § 7. Hecke’s Theorem on the Different -- §8. The Residue Theorem -- 7. Foundations of the Theory of Hermitian Forms -- §1. Basic Definitions -- § 2. Hermitian
Categories -- § 3. Quadratic Forms -- §4. Transfer and Reduction -- § 5. Hermitian Abelian Categories -- §6. Hermitian Forms over Skew Fields -- §7. Hyperbolic Forms and the Unitary Group -- §8. Alternating Forms and the Symplectic
Group -- §9. Witt’s Theorem -- § 10. The Krull-Schmidt Theorem -- §11. Examples and Applications -- 8. Simple Algebras and Involutions -- §1. Simple Rings and Modules -- §2. Tensor Products -- § 3. Central Simple Algebras. The Brauer
Group -- §4. Simple Algebras -- §5. Central Simple Algebras under Field Extensions. Reduced Norms and Traces -- §6. Examples -- §7. Involutions on Simple Algebras. The Classification Problem -- § 8. Existence of Involutions -- §9. The
Corestriction. Existence of Involutions of the Second Kind -- § 10. An Extension Theorem for Involutions -- §11. Quaternion Algebras -- §12. Cyclic Algebras -- §13. The Canonical Involution on the Group Algebra -- 9. Clifford Algebras
-- §1. Graded Algebras -- §2. Clifford Algebras -- § 3. The Spinor Norm -- §4. Quadratic Forms over Fields in Characteristic 2 -- 10. Hermitian Forms over Global Fields -- §1. Hermitian Forms over Commutative Fields and Quaternion
Algebras -- §2. Simple Algebras and Involutions over Local and Global Fields -- §3. Skew Hermitian Forms over Quaternion Fields -- §4. Skew Hermitian Forms over Global Quaternion Fields. -- §5. The Strong Approximation Theorem -- §6.
Hermitian Forms for Unitary Involutions. Statement of Results -- §7. Proof of the Weak Local Global Principle -- §8. Conclusion of the Proof
ISBN:9783642699719
Series:eBooks
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Series:Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics: 270
Keywords: Mathematics , Number theory , Mathematics , Number Theory
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Call number:SPRINGER-1985-9783540396284:ONLINE Show nearby items on shelf
Title:Séminaire d'Algèbre Paul Dubreil et Marie-Paule Malliavin Proceedings, Paris 1983–1984 (36ème Année)
Author(s):
Date:1985
Size:1 online resource (424 p.)
Note:10.1007/BFb0074534
Contents:Quasihomogene affine Varietäten für SL(2,?) -- Automorphismes des surfaces non completes, groupes fuchsiens et singularites quasihomogenes -- Quelques résultats et conjectures concernant les séries de Poincaré des invariants des
formes binaires -- Interpolation de Newton à plusieurs variables -- A constructive characterization of all optimal linear codes -- Actions of formal groups on formal schemes. Applications to control theory and combinatorics -- Complexe
bidualisant en algebre non commutative -- The K-theory of filtered rings and skew laurent extensions -- Microlocalisation algebrique -- to the algebraic theory of positive characteristic differential geometry -- Quadratic forms and
finite representation type -- The catenarian property of the polynomial rings over a Prüfer domain -- Ore sets in Noetherian rings -- D-anneaux et anneaux F-semi-parfaits -- Hereditary P.I. algebras
ISBN:9783540396284
Series:eBooks
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Series:Lecture Notes in Mathematics: 1146
Keywords: Mathematics , Algebra , Mathematics , Algebra
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Call number:SPRINGER-1984-9789400963696:ONLINE Show nearby items on shelf
Title:Methods in Ring Theory
Author(s):
Date:1984
Size:1 online resource (576 p.)
Note:10.1007/978-94-009-6369-6
Contents:R-Prüfer Rings and Approximation Theorems -- Certain Artinian Lattices Are Noetherian. Applications to the Relative Hopkins-Levitzki Theorem -- A Generalization of Semisimple Modules -- Graded Complete and Graded Henselian Rings --
Cyclic Classes in Relative Brauer Groups -- Simple Noetherian Non-Matrix Rings -- Group-Gradings of Categories -- Brauer Groups of Homogeneous Spaces I -- Simple Submodules in a Finite Direct Sum of Uniform Modules -- Functors of
Graded Rings -- Sur une Classe d’Algèbres Filtrées -- Some Special Class of Artin Rings of Finite Type -- Group Rings and Maximal Orders -- A Note on Infinite Torsion Primes of a Commutative Ring -- Applications of Kummer Theory
Without Roots of Unity -- The Index of Nility of a Matrix Ring Over a Ring With Bounded Index -- On Algebraic Derivations of Prime Rings -- Smooth Maximal Orders in Quaternion Algebras I -- Group Rings and Division Rings -- On Free
Subobjects of Skew Fields -- Herstein’s Lie and Jordan Theory Revisited -- Divisorially Graded Orders in a Simple Artinian Ring -- ? -Injective Modules and QF-3 Endomorphism Rings -- Group Actions on Rings: Some Classical Problems --
Links Between Maximal Ideals in Bounded Noetherian Prime Rings of Krull Dimension One -- Noetherian Subrings of Quotient Rings -- Stability Conditions for Cummutative Rings with Krull Dimension -- Cancellative Group-Graded Rings -- The
Automorphism Group of a Polynomial Algebra -- Auslander-Reiten Quivers for Some Artinian Torsion Theories and Integral Representations -- Automorphisms and Isomorphisms of Integral Group Rings of Finite Groups -- Self-Injective
Dimension of Serial Rings -- Smooth Affine PI Algebras -- Questions on Skew Fields -- Torsion Units in Group Rings -- On the Length of Decompositions of Central Simple Algebras in Tensor Products of Symbols -- A Duality Theorem for
Hopf Algebras -- Note on Central Class Groups of Orders Over Krull Domains -- On the Picard Group of a Quasi-Affine Scheme -- Duality Theory for Quasi-Injective Modules -- List of Participants
ISBN:9789400963696
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:NATO ASI Series, Series C: Mathematical and Physical Sciences: 129
Keywords: Mathematics , Algebra , Associative rings , Rings (Algebra) , Nonassociative rings , Mathematics , Algebra , Associative Rings and Algebras , Non-associative Rings and Algebras
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Call number:SPRINGER-1984-9783540391029:ONLINE Show nearby items on shelf
Title:Groups — Korea 1983 Proceedings of a Conference on Combinatorial Group Theory, held at Kyoungju, Korea, August 26–31, 1983
Author(s):
Date:1984
Size:1 online resource (190 p.)
Note:10.1007/BFb0099655
Contents:Algorithmically insoluble problems about finitely presented solvable groups, lie, and associative algebras -- On the simple groups of order less than 105 -- On some algorithmic problems for finitely presented groups and lie algebras
-- The concept of largeness in group theory II -- Extending groups via tree automorphisms -- HNN-constructing finite groups -- Analogues of the braid group -- Some uses of coset graphs -- Discontinuous groups -- Commutative quandles --
Metabelian groups of prime-power exponent -- Symmetric graphs and the classification of the finite simple groups -- Decision problems for infinite soluble groups -- Automorphisms and isomorphisms of integral group rings of finite
groups -- On induced isomorphisms of group rings -- Über Darstellungen von Elementen und Untergruppen in freien Produkten -- On the circle groups of finite nilpotent rings
ISBN:9783540391029
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Lecture Notes in Mathematics: 1098
Keywords: Mathematics , Group theory , Combinatorics , Mathematics , Group Theory and Generalizations , Combinatorics
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Call number:SPRINGER-1983-9783540386865:ONLINE Show nearby items on shelf
Title:Séminaire d’Algèbre Paul Dubreil et Marie-Paule Malliavin Proceedings, Paris 1982 (35ème Année)
Author(s):
Date:1983
Size:1 online resource (346 p.)
Note:10.1007/BFb0098924
Contents:Lectures on invariants, representations and lie algebras in systems and control theory -- Series de Poincare dans la theorie des invariants -- On the cohomology of locally symmetric hermitian spaces -- A study of the torsion-free part
of the cokernel from the operator acting on a D n-module -- The regular representations of the tame hereditary algebras -- Separating tubular series -- Higher even clifford algebras -- Modifications monomiales -- La serie de bass d’un
produit fibre d’Anneaux locaux -- Relative invariants for commutative rings -- Sur l’Extension RG ? R -- Modules sur les anneaux de Krull non commutatifs -- Localization of crossed-modules -- The division ring of fractions of a group
ring
ISBN:9783540386865
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Lecture Notes in Mathematics: 1029
Keywords: Mathematics , Algebra , Mathematics , Algebra
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Call number:SPRINGER-1981-9783540387374:ONLINE Show nearby items on shelf
Title:Séminaire d'Algèbre Paul Dubreil et Marie-Paule Malliavin Proceedings, Paris 1980 (33ème Année)
Author(s):
Date:1981
Size:1 online resource (476 p.)
Note:10.1007/BFb0090377
Contents:Invariant theory, representation theory, commutative algebra-ménage à trois -- On the construction of some relative invariants for CL(n) (n=6,7,8) by the decomposition of the Young diagrams -- Concentration under actions of algebraic
groups -- Some conjectures for root systems and finite coxeter groups -- Spectre du de Rham-Hodge sur l'espace projectif quaternionique -- Groupe de Lie p-adique, Immeuble et Cohomologie -- Report on normal bundles of curves in ?3 --
The bernstein class of modules on algebraic manifolds -- Anneaux d'opérateurs différentiels -- Factorialite et series formelles irreductibles ii -- Homologie d'anneaux locaux de dimension d'immersion 3 -- Dimensions cohomologiques
relieés aux foncteurs -- Genus and a riemann-roch theorem for non-commutative function fields in one variable -- Pour une geometrie algebrique non-commutative -- Sur la formule de Molien dans certaines algèbres enveloppantes --
Semiprime ideals in rings with finite group actions revisited -- Les modules artiniens et leurs enveloppes quasi-injectives -- The reduced rank in noetherian rings -- Prime ideals in group algebras of polycyclic-by-finite groups :
Vertices and sources -- Structure of integral group rings -- Standard monomial theory
ISBN:9783540387374
Series:eBooks
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Series:Lecture Notes in Mathematics: 867
Keywords: Mathematics , Algebra , Mathematics , Algebra
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Call number:SPRINGER-1980-9783540383345:ONLINE Show nearby items on shelf
Title:Ring Theory Antwerp 1980 Proceedings, University of Antwerp U.I.A. Antwerp, Belgium, May 6–9, 1980
Author(s):
Date:1980
Size:1 online resource (214 p.)
Note:10.1007/BFb0089114
Contents:Normalizing extensions I -- Normalizing extensions II -- Commutant des Modules de Longueur Finie sur Certaines Algèbres Filtrées -- Maximal orders applied to enveloping algebras -- Fxtensions of valuations on skew fields -- Extensions
of simple by simple unit-regular rings -- Invertible 2×2 matrices over skew polynomial rings -- Hereditary P. I. algebras -- Grade et Théorème d’intersection en algèbre Non commutative -- Théorème de Hopkins pour les Catégories de
Grothendieck -- The moore-penrose inverse for matrices over skew polynomial rings -- The lattice type of orders: A diagrammatic approach. I -- Arithmetically graded rings .I. -- Radicals and chain conditions -- Graded azumaya algebras
and brauer groups -- Birationality of P.I. rings and non-commutative varieties -- Skew power series rings and some homological properties of filtered rings
ISBN:9783540383345
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Series:Lecture Notes in Mathematics: 825
Keywords: Mathematics , Algebra , Mathematics , Algebra
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Call number:SPRINGER-1979-9783540355380:ONLINE Show nearby items on shelf
Title:Module Theory Papers and Problems from The Special Session Sponsored by The American Mathematical Society at The University of Washington Proceedings, Seattle, August 15–18, 1977
Author(s):
Date:1979
Size:1 online resource (244 p.)
Note:10.1007/BFb0063455
Contents:Cancellation for nonprojective modules -- Stable generation of modules -- Some aspects of Fuller's theorem -- On inversive localization -- Semicritical modules and k-primitive rings -- A note on loewy rings and chain conditions on
primitive ideals -- Decomposition of dual-continuous modules -- On the Gabriel dimension and subidealizer rings -- Big and small Cohen-Macaulay modules -- Rings of bounded module type -- Injective quotient rings of commutative rings --
Spectrum, topologies and sheaves for left noetherian rings -- Fully left bounded left Noetherian rings -- Bounded prime rings, Pseudo-Frobenius rings, the Jacobson radical of a ring -- Commutative Noetherian local rings -- Continuous
and dual-continuous modules -- Left stable left Noetherian rings -- Finitely generated algebras over a field -- Simple Noetherian rings -- Subidealizers -- Equivalence of matrices, prime rings, number of generators, state spaces
ISBN:9783540355380
Series:eBooks
Series:SpringerLink (Online service)
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Series:Lecture Notes in Mathematics: 700
Keywords: Mathematics , Mathematics , Mathematics, general
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Call number:SPRINGER-1979-9783540351818:ONLINE Show nearby items on shelf
Title:Commutative Rings whose Finitely Generated Modules Decompose
Author(s): Willy Brandal
Date:1979
Size:1 online resource (116 p.)
Note:10.1007/BFb0069021
Contents:Linearly compact modules and almost maximal rings -- h-Local domains -- Valuation rings and Bezout rings -- Basic facts about FGC rings and the local case -- Further facts about FGC rings and Torch rings -- The Zariski and Patch
topologies of the spectrum of a ring -- The Stone-Cech compactification of N -- Relating topology to the decomposition of modules -- The main theorem -- Valuations -- Long power series rings -- Maximally complete valuation domains --
Examples of maximal valuation rings -- Examples of almost maximal Bezout domains -- Examples of Torch rings
ISBN:9783540351818
Series:eBooks
Series:SpringerLink (Online service)
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Series:Lecture Notes in Mathematics: 723
Keywords: Mathematics , Commutative algebra , Commutative rings , Mathematics , Commutative Rings and Algebras
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Call number:SPRINGER-1979-9783540350200:ONLINE Show nearby items on shelf
Title:Séminaire d'Algèbre Paul Dubreil Proceedings, Paris 1977–78 (31ème Année)
Author(s):
Date:1979
Size:1 online resource (456 p.)
Note:10.1007/BFb0071048
Contents:Finitely presented soluble groups -- Actions de Groupes -- Théorème d'induction de Brauer et application au calcul des caractères modulaires -- Groupes algebriques infinitesimaux resolubles et leurs representations lineaires
irreductibles -- The irreducible representations of the Weyl algebra A1 -- Noetherian algebras and the Nullstellensatz -- Orbites dans le spectre primitif de l'algebre enveloppante d'une algebre de lie -- Series formelles tordues et
conditions de chaines -- Les théorèmes de Cohen-Seidenberg en algèbre non commutative -- Classes d'anneaux contenant les V-anneaux et les anneaux absolument plats -- Un ideal maximal de l'anneau des endomorphismes d'un espace vectoriel
de dimension infinie -- Prolongements de Q-anneaux de Matlis -- La classe des anneaux excellents est-elle fermee par limite inductive noetherienne plate ? -- La cinquième déflection d'un anneau local noethérien -- Necessary conditions
for the existence of dualizing complexes in commutative algebra -- Deformation of certain Gorenstein singularities -- Algèbre homologique des anneaux locaux à corps résiduels de caractéristique deux -- Homomorphismes d'anneaux locaux
et homologie -- Some complex constructions with applications to Poincaré series -- Relations between the Poincaré-Betti series of loop spaces and of local rings -- Rationalité de certaines séries de Poincaré -- Généralisation d'un
critère de Pontryagin concernant les groupes sans torsion dénombrables à des modules sans torsion sur des anneaux de Dedekind. Conditions de rang, de type, de chaînes ascendantes -- Idéaux bilatères et centre des anneaux de polynômes
de Ore sur les anneaux quasi-simples -- Caténarité et théorème d'intersection en algèbre non commutative -- Sur les anneaux de groupe héréditaires -- Torsion et localisation de groupes arbitraires
ISBN:9783540350200
Series:eBooks
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Series:Lecture Notes in Mathematics: 740
Keywords: Mathematics , Mathematics , Mathematics, general
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Call number:SPRINGER-1979-9780387774879:ONLINE Show nearby items on shelf
Title:Universal Algebra
Author(s): George Grätzer
Date:1979
Publisher:New York, NY : Springer New York
Size:1 online resource (583 p.)
Note:10.1007/978-0-387-77487-9
Contents:Basic Concepts -- Subalgebras and Homomorphisms -- Partial Algebras -- Constructions of Algebras -- Free Algebras -- Independence -- Elements of Model Theory -- Elementary Properties of Algebraic Constructions -- Free Structures --
Appendix 1. General Survey -- Appendix 2. The Problems -- Appendix 3. Congruence Varieties -- Appendix 4. Equational Logic by Walter Taylor -- Appendix 5. Primality the influence of Boolean Algebras in Universal Algebra -- Appendix 6
Equational Compactness -- Appendix 7 The Independence Proof
ISBN:9780387774879
Series:eBooks
Series:SpringerLink (Online service)
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Keywords: Mathematics , Algebra , Commutative algebra , Commutative rings , Ordered algebraic structures , Mathematics , Algebra , Commutative Rings and Algebras , Order, Lattices, Ordered Algebraic Structures
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Call number:SPRINGER-1976-9783540379836:ONLINE Show nearby items on shelf
Title:Noncommutative Ring Theory Papers presented at the International Conference Held at Kent State University April 4–5, 1975
Author(s):
Date:1976
Size:1 online resource (216 p.)
Note:10.1007/BFb0080303
Contents:Some aspects of noncomutative localization -- Zero-divisors in tensor products -- Regular rings and rank functions -- Some aspects of noncommutative noetherian rings -- Certain injectives are artinian -- Artinian quotient rings of
macaulay rings -- Cyclic and faithful objects in quotient categories with applications to noetherian simple or asano rings -- Prime singular-splitting rings with finiteness conditions -- Problem session on regular rings -- Problems
ISBN:9783540379836
Series:eBooks
Series:SpringerLink (Online service)
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Series:Lecture Notes in Mathematics: 545
Keywords: Mathematics , Commutative algebra , Commutative rings , Nonassociative rings , Rings (Algebra) , Mathematics , Commutative Rings and Algebras , Non-associative Rings and Algebras
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Call number:SPRINGER-1976-9783540379645:ONLINE Show nearby items on shelf
Title:Algebraic K-Theory Proceedings of the Conference Held at Northwestern University Evanston, January 12–16, 1976
Author(s):
Date:1976
Size:1 online resource (414 p.)
Note:10.1007/BFb0079990
Contents:An example in the theory of algebraic cycles spencer bloch -- SK1 of commutative normed algebras -- The K-theory of some reducible affine curves: A combinatorial approach -- SKn of orders and Gn of finite rings -- K2 of a global field
consists of symbols -- Generators and relations for K2 of a division ring -- Injective stability for K2 -- Les matrices monomiales et le groupe de whitehead ?h2 -- Finitely presented groups of matrices -- Homology sphere bordism and
quillen plus construction -- Letter from Quillen to Milnor on -- Characteristic classes of representations -- Higher algebraic K-theory: II -- Continuous cohomology and p-adic K-theory -- Cohomology of groups -- On the homology and
cohomology of the orthogonal and symplectic groups over a finite field of odd characteristic -- Homology of classical groups over a finite field -- Group cohomology classes with differential form coefficients -- Stability for H2 (Sun)
-- Homological stability for classical groups over finite fields -- Hermitian K-theory in topology: A survey of some recent results -- Higher witt groups: A survey -- The exact sequence of a localization for witt groups -- Orthogonal
representations on positive definite lattices -- The computation of surgery groups of finite groups with abelian 2-hyperelementary subgroups
ISBN:9783540379645
Series:eBooks
Series:SpringerLink (Online service)
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Series:Lecture Notes in Mathematics: 551
Keywords: Mathematics , Category theory (Mathematics) , Homological algebra , Algebraic topology , Mathematics , Category Theory, Homological Algebra , Algebraic Topology
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Call number:SPRINGER-1975-9783642660665:ONLINE Show nearby items on shelf
Title:Rings of Quotients An Introduction to Methods of Ring Theory
Author(s): Bo Stenström
Date:1975
Size:1 online resource (309 p.)
Note:10.1007/978-3-642-66066-5
Contents:Notations and Conventions -- I. Modules -- § 1. Basic Definitions -- § 2. Sums and Products of Modules -- § 3. Finitely Generated Modules and Noetherian Modules -- § 4. Categories and Functors -- § 5. Exactness of Functors between
Module Categories -- § 6. Projective and Injective Modules -- § 7. Semi-Simple Modules and Rings -- § 8. Tensor Products -- § 9. Bimodules -- § 10. Flat Modules -- § 11. Pure Submodules -- § 12. Regular Rings -- § 13. Coherent Rings --
Exercises -- II. Rings of Fractions -- § 1. The Ring of Fractions -- § 2. Orders in a Semi-Simple Ring -- § 3. Modules of Fractions -- § 4. Invertible Ideals and Hereditary Orders -- Exercises -- III. Modular Lattices -- § 1. Lattices
-- § 2. Modularity -- § 3. Lattices with Chain Condition -- § 4. Distributive Lattices -- § 5. Continuous Lattices -- § 6. Pseudo-Complemented Lattices -- § 7. Closure Operators -- § 8. Galois Connections -- Exercises -- IV. Abelian
Categories -- § 1. Equivalence of Categories -- § 2. Kernels and Cokernels -- § 3. Products and Coproducts -- § 4. Abelian Categories -- § 5. Pullbacks and Pushouts -- § 6. Generators and Cogenerators -- § 7. Functor Categories -- § 8.
Limits and Colimits -- § 9. Adjoint Functors -- § 10. Morita Equivalence -- Exercises -- V. Grothendieck Categories -- § 1. Exactness of Direct Limits -- § 2. Injective Envelopes -- § 3. Finitely Generated Objects -- § 4. Locally
Noetherian Categories -- § 5. The Krull-Remak-Schmidt-Azumaya Theorem -- § 6. Spectral Categories -- § 7. The Spectral Category of a Grothendieck Category -- Exercises -- VI. Torsion Theory -- § 1. Preradicals -- § 2. Torsion Theories
-- § 3. Hereditary Torsion Theories -- § 4. Linear Topologies -- § 5. Gabriel Topologies -- § 6. Examples of Gabriel Topologies -- § 7. Stable Torsion -- § 8. TTF-Classes -- § 9. ?-Divisible Modules -- Exercises -- VII. Hereditary
Torsion Theories for Noetherian Rings -- § 1. Associated Prime Ideals -- § 2. Fully Bounded Noetherian Rings -- § 3. Topologies for a Fully Bounded Noetherian Ring -- § 4. Artin-Rees Modules and Stable Topologies -- § 5. Auxiliary
Results on Commutative Localization -- § 6. The Topologies ?Mn for a Commutative Noetherian Ring -- Exercises -- VIII. Simple Torsion Theories -- § 1. The Jacobson Radical and Artinian Rings -- § 2. Semi-Artinian Modules and Rings -- §
3. Simple Torsion Theories -- § 4. Semi-Perfect Rings -- § 5. Perfect Rings -- § 6. Hereditary Torsion Theories for a Perfect Ring -- Exercises -- IX. Rings and Modules of Quotients -- § 1. Construction of Modules of Quotients -- § 2.
?-Injective Envelopes -- § 3. The Ring of Quotients is a Bicommutator -- § 4. The Lattice of Saturated Submodules -- § 5. ?-Invertible Ideals -- Exercises -- X. The Category of Modules of Quotients -- § 1. Giraud Subcategories -- § 2.
Gabriel Topologies and Giraud Subcategories -- § 3. Rings of Quotients of Morita Equivalent Rings -- § 4. Representation of Grothendieck Categories -- Exercises -- XI. Perfect Localizations -- § 1. Epimorphisms of Rings -- § 2. Flat
Epimorphisms of Rings -- § 3. Perfect Gabriel Topologies -- § 4. The Maximal Flat Epimorphic Ring of Quotients -- § 5. The Maximal Ring of Quotients as a Perfect Localization -- § 6. 1-Topologies and Rings of Fractions -- § 7. Finite
Localizations -- § 8. The Endomorphism Ring of a Finitely Generated Projective Module -- Exercises -- XII. The Maximal Ring of Quotients of a Non-Singular Ring -- § 1. Standard Representation of Spectral Categories -- § 2. The Maximal
Ring of Quotients -- § 3. The Maximal Ring of Quotients of a Boolean Ring -- § 4. The Lattice of Essentially Closed Ideals -- § 5. The Maximal Ring of Quotients of a Reduced Ring -- § 6. Flatness of the Maximal Ring of Quotients -- §
7. Imbedding Non-Singular Modules in Free Modules -- Exercises -- XIII. Finiteness Conditions on Mod-(A, ?) -- § 1. Compact Lattices of Saturated Submodules -- § 2. ?-Noetherian Rings -- § 3. The Goldie Topology -- § 4. P-Noetherian
Rings -- § 5. The Canonical Topology of a Krull Domain -- Exercises -- XIV. Self-Injective Rings -- § 1. The Endomorphism Ring of an Injective Module -- § 2. Self-Injective Rings and Annihilator Conditions -- § 3. Quasi-Frobenius Rings
-- § 4. Self-Injective Maximal Rings of Quotients -- Exercises -- XV. Classical Rings of Quotients -- § 1. Semi-Prime Ideals and the Prime Radical -- § 2. Rings of Quotients of Quotient Rings -- § 3. Orders in a Semi-Primary Ring -- §
4. Noetherian Orders in an Artinian Ring -- § 5. Orders in Self-Injective Rings -- § 6. Rings of Quotients of Group Algebras -- Exercises
ISBN:9783642660665
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Series:Die Grundlehren der mathematischen Wissenschaften, Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete: 217
Keywords: Mathematics , Algebra , Mathematics , Algebra
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Call number:SPRINGER-1974-9781461261018:ONLINE Show nearby items on shelf
Title:Algebra
Author(s): Thomas W Hungerford
Date:1974
Publisher:New York, NY : Springer New York
Size:1 online resource (504 p.)
Note:10.1007/978-1-4612-6101-8
Contents:Introduction: Prerequisites and Preliminaries -- 1. Logic -- 2. Sets and Classes -- 3. Functions -- 4. Relations and Partitions -- 5. Products -- 6. The Integers -- 7. The Axiom of Choice, Order and Zorn’s Lemma -- 8. Cardinal Numbers
-- I: Groups -- 1. Semigroups, Monoids and Groups -- 2. Homomorphisms and Subgroups -- 3. Cyclic Groups -- 4. Cosets and Counting -- 5. Normality, Quotient Groups, and Homomorphisms -- 6. Symmetric, Alternating, and Dihedral Groups --
7. Categories: Products, Coproducts, and Free Objects -- 8. Direct Products and Direct Sums -- 9. Free Groups, Free Products, Generators & Relations -- II: The Structure of Groups -- 1. Free Abelian Groups -- 2. Finitely Generated
Abelian Groups -- 3. The Kruli-Schmidt Theorem -- 4. The Action of a Group on a Set -- 5. The Sylow Theorems -- 6. Classification of Finite Groups -- 7. Nilpotent and Solvable Groups -- 8. Normal and Subnormal Series -- III: Rings --
1. Rings and Homomorphisms -- 2. Ideals -- 3. Factorization in Commutative Rings -- 4. Rings of Quotients and Localization -- 5. Rings of Polynomials and Formal Power Series -- 6. Factorization in Polynomial Rings -- IV: Modules -- 1.
Modules, Homomorphisms and Exact Sequences -- 2. Free Modules and Vector Spaces -- 3. Projective and Injective Modules -- 4. Horn and Duality -- 5. Tensor Products -- 6. Modules over a Principal Ideal Domain -- 7. Algebras -- V: Fields
and Galois Theory -- 1. Field Extensions -- 2. The Fundamental Theorem -- 3. Splitting Fields, Algebraic Closure and Normality -- 4. The Galois Group of a Polynomial -- 5. Finite Fields -- 6. Separability -- 7. Cyclic Extensions -- 8.
Cyclotomic Extensions -- 9. Radical Extensions -- VI: The Structure of Fields -- 1. Transcendence Bases -- 2. Linear Disjointness and Separability -- VII: Linear Algebra -- 1. Matrices and Maps -- 2. Rank and Equivalence -- 3.
Determinants -- 4. Decomposition of a Single Linear Transformation and Similarity -- 5. The Characteristic Polynomial, Eigenvectors and Eigenvalues -- VIII: Commutative Rings and Modules -- 1. Chain Conditions -- 2. Prime and Primary
Ideals -- 3. Primary Decomposition -- 4. Noetherian Rings and Modules -- 5. Ring Extensions -- 6. Dedekind Domains -- 7. The Hilbert Nullstellensatz -- IX: The Structure of Rings -- 1. Simple and Primitive Rings -- 2. The Jacobson
Radical -- 3. Semisimple Rings -- 4. The Prime Radical Prime and Semiprime Rings -- 5. Algebras -- 6. Division Algebras -- X: Categories -- 1. Functors and Natural Transformations -- 2. Adjoint Functors -- 3. Morphisms -- List of
Symbols
ISBN:9781461261018
Series:eBooks
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Series:Graduate Texts in Mathematics: 73
Keywords: Mathematics , Algebra , Mathematics , Algebra
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Call number:SPRINGER-1973-9783642884054:ONLINE Show nearby items on shelf
Title:The Divisor Class Group of a Krull Domain
Author(s): Robert M Fossum
Date:1973
Size:1 online resource (150 p.)
Note:10.1007/978-3-642-88405-4
Contents:I. Krull Domains -- § 1. The Definition of a Krull Ring -- § 2. Lattices -- § 3. Completely Integrally Closed Rings -- § 4. Krull’s Normality Criterion and the Mori-Nagata Integral Closure Theorem -- § 5. Divisorial Lattices and the
Approximation Theorem -- II. The Divisor Class Group and Factorial Rings -- § 6. The Divisor Class Group and its Functorial Properties -- § 7. Nagata’s Theorem -- § 8. Polynomial Extensions -- § 9. Regular Local Rings -- § 10. Graded
Krull Domains and Homogeneous Ideals -- §11. Quadratic Forms -- §12. Murthy’s Theorem -- III. Dedekind Domains -- § 13. Dedekind Domains and a Generalized Approximation Theorem -- § 14. Every Abelian Group is an Ideal Class Group -- §
15. Presentations of Ideal Class Groups of Dedekind Domains -- IV. Descent -- § 16. Galois Descent -- § 17. Radical Descent -- V. Completions and Formal Power Series Extensions -- § 18. The Picard Group -- § 19. Completions, Formal
Power Series and Danilov’s Results. -- Appendix I: Terminology and Notation -- Appendix II: List of Results
ISBN:9783642884054
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Ergebnisse der Mathematik und ihrer Grenzgebiete: 74
Keywords: Mathematics , Commutative algebra , Commutative rings , Group theory , Mathematics , Commutative Rings and Algebras , Group Theory and Generalizations
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Call number:SPRINGER-1973-9783642870811:ONLINE Show nearby items on shelf
Title:Infinite Linear Groups An Account of the Group-theoretic Properties of Infinite Groups of Matrices
Author(s): Bertram A. F Wehrfritz
Date:1973
Size:1 online resource (232 p.)
Note:10.1007/978-3-642-87081-1
Contents:1. Basic Concepts -- 2. Some Examples of Linear Groups -- 3. Soluble Linear Groups -- 4. Finitely Generated Linear Groups -- 5. CZ-Groups and the Zariski Topology -- 6. The Homomorphism Theorems -- 7. The Jordan Decomposition and
Splittable Linear Groups -- 8. The Upper Central Series in Linear Groups -- 9. Periodic Linear Groups -- 10. Rank Restrictions, Varietal Properties and Wreath Products -- 11. Supersoluble and Locally Supersoluble Linear Groups -- 12. A
Localizing Technique and Applications -- 13. Module Automorphism Groups over Commutative Rings -- 14. Appendix on Algebraic Groups -- Suggestions for Further Reading
ISBN:9783642870811
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Ergebnisse der Mathematik und ihrer Grenzgebiete: 76
Keywords: Mathematics , Group theory , Matrix theory , Algebra , Topological groups , Lie groups , Mathematics , Linear and Multilinear Algebras, Matrix Theory , Group Theory and Generalizations , Topological Groups, Lie Groups
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Call number:SPRINGER-1972-9789400981799:ONLINE Show nearby items on shelf
Title:Introduction to Algebra
Author(s): R Kochendörffer
Date:1972
Size:1 online resource (414 p.)
Note:10.1007/978-94-009-8179-9
Contents:1. Basic concepts -- 1.1. Sets -- 1.2. Relations -- 1.3. Mappings -- 1.4. Operations -- 1.5. Algebraic systems -- 2. The integers -- 2.1. The natural numbers and the integers -- 2.2. Divisibility. Prime numbers -- 2.3. The greatést common divisor - - 2.4. Prime factorization -- 2.5. Congruences. Residue classes -- 2.6. The residue class ring -- 2.7. Simultaneous congruences. Euler’s function -- 3. Groups -- 3.1. Semigroups -- 3.2. Groups -- 3.3. Isomorphisms. Automorphisms -- 3.4. Embedding of abe lian semigroups in groups -- 3.5. Subgroups -- 3.6. Cyclic groups -- 3.7. Homomorphisms -- 3.8. Subnormal series -- 3.9. Direct products -- 3.10. Permutation groups -- 3.11. Sylow subgroups and p-groups -- 3.12. Endomorphisms and operators -- 3.13. Vector spaces. Modules -- 4. Rings. Integral domains -- 4.1. Definitions and examples -- 4.2. Homomorphisms -- 4.3. Commutative rings. Integral domains -- 4.4. Principal ideal rings -- 4.5. Euclidean rings -- 4.6. Fields of quotients -- 4.7. Prime
fields. Characteristic -- 5. Polynomials -- 5.1. Polynomials in one indeterminate -- 5.2. Polynomials over fields -- 5.3. Polynomials over integral domains. -- 5.4. Roots. The derivative -- 5.5. Polynomials in several indeterminates -- 5.6. Symmetri c polynomials -- 5.7. The resultant and the discriminant -- 6. Fields -- 6.1. Adjunction -- 6.2. Algebraic extension fields -- 6.3. Construction of extension fields -- 6.4. Normal extensions -- 6.5. Separable and inseparable extensions -- 6.6. Galois theo ry -- 6.7. Cyclotomic fields -- 6.8. Galois fields -- 7. Galois theory of equations -- 7.1. The Galois group of a polynomial -- 7.2. Solubility of equations by radicals -- 7.3. Quadratic, cubic, and quartic equations -- 7.4. Constructions by ruler and com pass -- 8. Order and valuations -- 8.1. Ordered fields -- 8.2. Formally real fields -- 8.3. Valuations -- 9. Modules -- 9.1. Elementary divisors -- 9.2. Modules over principal ideal rings -- 9.3. Endomorphisms of vector spaces -- 9.4.
Finiteness conditions -- 9.5. Algebraic integers -- 10. Algebras -- 10.1. Basic definitions -- 10.2. The radical -- 10.3. Semi-simple rings -- 10.4. Simple rings -- 10.5. Division algebras over the field of the real numbers -- 10.6. Representation m odules -- 10.7. Representations of semi-simple algebras -- 11. Lattices -- 11.1. Lattices and partially ordered sets -- 11.2. Modular lattices -- 11.3. Distributive lattices
ISBN:9789400981799
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Keywords: Mathematics , Algebra , Mathematics , Mathematics , Algebra , Mathematics Education
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Call number:SPRINGER-1971-9783540364849:ONLINE Show nearby items on shelf
Title:Separable Algebras Over Commutative Rings
Author(s): Frank DeMeyer
Date:1971
Size:1 online resource (166 p.)
Note:10.1007/BFb0061226
Contents:Preliminaries -- Central separable algebras and the brauer group -- Galois theory -- The six-term exact sequence -- Applications and remarks
ISBN:9783540364849
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Lecture Notes in Mathematics: 181
Keywords: Mathematics , Algebra , Mathematics , Algebra
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Call number:SPRINGER-1964-9781461298724:ONLINE Show nearby items on shelf
Title:Lectures in Abstract Algebra III. Theory of Fields and Galois Theory
Author(s): Nathan Jacobson
Date:1964
Publisher:New York, NY : Springer New York
Size:1 online resource (324 p.)
Note:10.1007/978-1-4612-9872-4
Contents:1. Extension of homomorphisms -- 2. Algebras -- 3. Tensor products of vector spaces -- 4. Tensor product of algebras -- I: Finite Dimensional Extension Fields -- 1. Some vector spaces associated with mappings of fields -- 2. The Jacobson-Bourbaki co rrespondence -- 3. Dedekind independence theorem for isomorphisms of a field -- 4. Finite groups of automorphisms -- 5. Splitting field of a polynomial -- 6. Multiple roots. Separable polynomials -- 7. The “fundamental theorem” of Galois theory -- 8. Normal extensions. Normal closures -- 9. Structure of algebraic extensions. Separability -- 10. Degrees of separability and inseparability. Structure of normal extensions -- 11. Primitive elements -- 12. Normal bases -- 13 Finite fields -- 14. Regular rep resentation, trace and norm -- 15. Galois cohomology -- 16 Composites of fields -- II: Galois Theory of Equations -- 1. The Galois group of an equation -- 2. Pure equations -- 3. Galois’ criterion for solvability by radicals -- 4. The general
equation of n-th degree -- 5. Equations with rational coefficients and symmetric group as Galois group -- III: Abelian Extensions -- 1. Cyclotomic fields over the rationals -- 2. Characters of finite commutative groups -- 3. Kummer extensions -- 4. Witt vectors -- 5. Abelian p-extensions -- IV: Structure Theory of Fields -- 1. Algebraically closed fields -- 2. Infinite Galois theory -- 3. Transcendency basis -- 4. Lüroth’s theorem -- 5. Linear disjointness and separating transcendency bases -- 6. Derivations -- 7. Derivations, separability and p-independence -- 8. Galois theory for purely inseparable extensions of exponent one -- 9. Higher derivations -- 10. Tensor products of fields -- 11. Free composites of fields -- V: Valuation Theory -- 1. R eal valuations -- 2. Real valuations of the field of rational numbers -- 3. Real valuations of ?(x) which are trivial in ? -- 4. Completion of a field -- 5. Some properties of the field of p-adic numbers -- 6. Hensel’s lemma -- 7. Construction
of complete fields with given residue fields -- 8. Ordered groups and valuations -- 9. Valuations, valuation rings, and places -- 10. Characterization of real non-archimedean valuations -- 11. Extension of homomorphisms and valuations -- 12. Applica tion of the extension theorem: Hilbert Nullstellensatz -- 13. Application of the extension theorem: integral closure -- 14. Finite dimensional extensions of complete fields -- 15. Extension of real valuations to finite dimensional extension fields -- 16. Ramification index and residue degree -- VI: Artin-Schreier Theory -- 1. Ordered fields and formally real fields -- 2. Real closed fields -- 3. Sturm’s theorem -- 4. Real closure of an ordered field -- 5. Real algebraic numbers -- 6. Positive definite r ational functions -- 7. Formalization of Sturm’s theorem. Resultants -- 8. Decision method for an algebraic curve -- 9. Equations with parameters -- 10. Generalized Sturm’s theorem. Applications -- 11. Artin-Schreier characterization of real
closed fields -- Suggestions for further reading
ISBN:9781461298724
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Graduate Texts in Mathematics: 32
Keywords: Mathematics , Algebra , Mathematics , Algebra
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Call number:SPRINGER-1960-9783662292440:ONLINE Show nearby items on shelf
Title:Commutative Algebra Volume II
Author(s): Oscar Zariski
Date:1960
Size:1 online resource (416 p.)
Note:10.1007/978-3-662-29244-0
Contents:Valuation Theory -- Polynomial and Power Series Rings -- Local Algebra
ISBN:9783662292440
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Graduate Texts in Mathematics: 29
Keywords: Mathematics , Commutative algebra , Commutative rings , Mathematics , Commutative Rings and Algebras
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