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SPIRES-BOOKS: FIND KEYWORD COMMUTATIVE RINGS *END*INIT* use /tmp/qspiwww.webspi1/31578.164 QRY 131.225.70.96 . find keyword commutative rings ( 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-2014-9781493909254:ONLINE Show nearby items on shelf
Title:Commutative Algebra [electronic resource] : Recent Advances in Commutative Rings, Integer-Valued Polynomials, and Polynomial Functions
Author(s): Marco Fontana
Sophie Frisch
Sarah Glaz
Date:2014
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:This volume presents a multi-dimensional collection of articles highlighting recent developments in commutative algebra. It also includes an extensive bibliography and lists a substantial number of open problems that point tofuture directions of rese arch in the represented subfields. The contributions cover areas in commutative algebra that have flourished in the last few decades and are not yet well represented in book form. Highlighted topics andresearch methods include Noetherian and non- Noetheri an ring theory as well as integer-valued polynomials and functions. Specific topics include: Homological dimensions of Prfer-like rings Quasi complete rings Total graphs of rings Properties of prime ideals over various rings Bases for integer-valued p olynomials Boolean subrings The portable property of domains Probabilistic topics inIntn(D) Closure operations in Zariski-Riemann spaces of valuation domains Stability of domains Non-Noetherian grade Homotopy in integer-valued polynomials Localiza tions of global propertiesof rings Topics in integral closure Monoids and submonoids of domains The book includes twenty articles written by many of the most prominent researchers in the field. Most contributions are authored by attendees ofthe conferen ce in commutative algebra held at the Graz University of Technology in December 2012. There is also a small collection of invited articles authored by those who did not attend the conference. Following the model of the Grazconference, the volume contains a number of comprehensive survey articles along with related research articles featuring recent results that have not yet been published elsewhere
Contents:Preface
Weak global dimension of Prfer
like rings (K. Adarbeh, S
E. Kabbaj)
Quasi
complete semilocal rings and modules (D.D. Anderson)
On the total graph of a ring and its related graphs: A survey (A. Badawi)
Prime ideals in polynomials and power series rings over Noetherian domains
Integer
valued polynomials: Looking for regular bases (J
L. Chabert)
On Boolean subrings of rings (I. Chajda, G. Eigenthaler)
On a new class of integral domains with the portable property (D.E. Dobbs, G. Picavet, M. Picavet
L'Hermitte)
The probability that Intn(D) is free (J. Elliott
ISBN:9781493909254
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Algebraic topology
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Call number:SPRINGER-2014-9781493906260:ONLINE Show nearby items on shelf
Title:Connections Between Algebra, Combinatorics, and Geometry [electronic resource]
Author(s): Susan M Cooper
Sean Sather-Wagstaff
Date:2014
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:Commutative algebra, combinatorics, and algebraic geometry are thriving areas of mathematical research with a rich history of interaction. Connections Between Algebra, Combinatorics,and Geometry contains lecture notes, alongwith exercises andsolution s, from the Workshop on Connections Between Algebra and Geometry held at the University of Regina from May 29-June 1, 2012. It also contains research and survey papers from academics invited to participatein the companion Special Session on Interactions B etween Algebraic Geometry and Commutative Algebra, which was part of the CMS Summer Meeting at the University of Regina held June 23, 2012, and the meeting Further ConnectionsBetween Algebra and Geometry, which was held at the North Dakota State Universit y, February 23, 2013. This volume highlights three mini-courses in the areas of commutative algebra and algebraic geometry: differential graded commutativealgebra, secant varieties, and fat points and symbolic powers. Itwill serve asausefulresourcefor gra duate students andresearchers who wish toexpand their knowledge of commutative algebra, algebraicgeometry,combinatorics, and the intricacies of their intersection.
Contents:Preface
Differential Graded Commutative Algebra
Secant Varieties
Fat Points and Symbolic Powers
An Introduction to Stanley
Reisner Rings
Combinatorial Resolutions
Geometric Properties of the Tor Algebra Structure for Trivariate Monomial Ideals
Interactions Between Linear Algebra and Algebraic Geometry
Fat Points
Primary Decomposition of Certain Permanental Ideals
ISBN:9781493906260
Series:eBooks
Series:SpringerLink
Series:Springer Proceedings in Mathematics & Statistics, 2194-1009 : v76
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Algebra
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Call number:SPRINGER-2013-9781461459873:ONLINE Show nearby items on shelf
Title:Introduction to Commutative Algebra and Algebraic Geometry [electronic resource]
Author(s): Ernst Kunz
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Birkhuser
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Originally published in 1985, this classic textbook is an English translation of Einfhrung in die kommutative Algebra und algebraische Geometrie. As part of the Modern Birkhuser Classics series, the publisher is proud to makeIntroduction to Commutati ve Algebra and Algebraic Geometry available to a wider audience. Aimed at students who have taken a basic course in algebra, the goal of the text is to present important results concerning the representationof algebraic varieties as intersections of the least possible number of hypersurfaces anda closely related problemwith the most economical generation of ideals in Noetherian rings. Along the way, one encounters many basicconcepts of commutative algebra and algebraic geometry and proves many facts whic h can then serve as a basic stock for a deeper study of these subjects
Note:Springer eBooks
Contents:Foreword
Preface
Preface to the English Edition
Terminology
Algebraic varieties
Dimension
Regular and rational functions on algebraic varieties
The local
global principle in commutative algebra
On the number of equations needed to describe an algebraic variety
Regular and singular points of algebraic varieties
Projective Resolutions
Bibliography
List of Symbols
Index.
ISBN:9781461459873
Series:e-books
Series:SpringerLink (Online service)
Series:Modern Birkhuser Classics
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Geometry, algebraic
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Call number:SPRINGER-2013-9781447148296:ONLINE Show nearby items on shelf
Title:Algebraic Geometry and Commutative Algebra [electronic resource]
Author(s): Siegfried Bosch
Date:2013
Publisher:London : Springer London : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Algebraic geometry is a fascinating branch of mathematics that combines methods from both algebra and geometry. It transcends the limited scope of pure algebra by means of geometric construction principles. Moreover,Grothendiecks schemes invented in the late 1950s allowed the application of algebraic-geometric methods in fields that formerly seemed to be far away from geometry (algebraic number theory, for example). The new techniques paved theway to spectacular progress such as the proof of Fermats Last Theorem by Wiles and Taylor. The scheme-theoretic approach to algebraic geometry is explained for non-experts whilst more advanced readers can use the book to broadentheir view on the subject. A separate part studies the necessary prerequisites from commutative algebra. The book provides an accessible and self-contained introduction to algebraic geometry, up to an advanced level. Every chapter ofthe book is preceded by a motivating introduction with an informal discussion of the contents. Typical exa mples and an abundance of exercises illustrate each section. Therefore the book is an excellent solution for learning by yourselfor for complementing knowledge that is already present. It can equally be used as a convenient source for courses and seminars or as supplemental literature
Note:Springer eBooks
Contents:Rings and Modules
The Theory of Noetherian Rings
Integral Extensions
Extension of Coefficients and Descent
Homological Methods: Ext and Tor
Affine Schemes and Basic Constructions
Techniques of Global Schemes
Etale and Smooth Morphisms
Projective Schemes and Proper Morphisms
ISBN:9781447148296
Series:e-books
Series:SpringerLink (Online service)
Series:Universitext, 0172-5939
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Algebra
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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-2012-9781447127307:ONLINE Show nearby items on shelf
Title:Finitely Generated Abelian Groups and Similarity of Matrices over a Field [electronic resource]
Author(s): Christopher Norman
Date:2012
Publisher:London : Springer London
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:At first sight, finitely generated abelian groups and canonical forms of matrices appear to have little in common. However, reduction to Smith normal form, named after its originator H.J.S.Smith in 1861, is a matrix version ofthe Euclidean algorithm and is exactly what the theory requires in both cases. Starting with matrices over the integers, Part1 of this book provides a measured introduction to such groups: two finitely generated abelian groups areisomorphic if and only if their invariant factor sequences are identical. The analogous theory of matrix similarity over a field is then developed in Part2 starting with matrices having polynomial entries: two matrices over a fieldare similar if and only if their rational canonical forms are equal. Unde r certain conditions each matrix is similar to a diagonal or nearly diagonal matrix, namely its Jordan form. The reader is assumed to be familiar with theelementary properties of rings and fields. Also a knowledge of abstract linear algebra including vect or spaces, linear mappings, matrices, bases and dimension is essential, although much of the theory is covered in the text but froma more general standpoint: the role of vector spaces is widened to modules over commutative rings. Based on a lecture course taught by the author for nearly thirty years, the book emphasises algorithmic techniques and features numerousworked examples and exercises with solutions. The early chapters form an ideal second course in algebra for second and third year undergraduates . The later chapters, which cover closely related topics, e.g. field extensions,endomorphism rings, automorphism groups, and variants of the canonical forms, will appeal to more advanced students. The book is a bridge between linear and abstract algebra
Note:Springer eBooks
Contents:Part 1 :Finitely Generated Abelian Groups: Matrices with Integer Entries: The Smith Normal Form
Basic Theory of Additive Abelian Groups
Decomposition of Finitely Generated Z
Modules. Part 2: Similarity of Square Matrices over a Field: The Polynomial Ring F[x]and Matrices over F[x]
F[x] Modules: Similarity of t xtMatrices over a Field F
Canonical Forms and Similarity Classes of Square Matrices over a Field.
ISBN:9781447127307
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Undergraduate Mathematics Series, 1615-2085
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Field theory (Physics) , Group theory , Matrix theory , Algorithms
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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-2011-9783642174049:ONLINE Show nearby items on shelf
Title:Modular Invariant Theory [electronic resource]
Author(s): H.E.A. Eddy Campbell
David L Wehlau
Date:2011
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This book covers the modular invariant theory of finite groups, the case when the characteristic of the field divides the order of the group. It explains a theory that is more complicated than the study of the classicalnon-modular case, and it descri bes many open questions. Largely self-contained, the book develops the theory from its origins up to modern results. It explores many examples, illustrating the theory and its contrast with the betterunderstood non-modular setting. It details techniques f or the computation of invariants for many modular representations of finite groups, especially the case of the cyclic group of prime order. It includes detailed examples of manytopics as well as a quick survey of the elements of algebraic geometry and com mutative algebra as they apply to invariant theory. The book is aimed at both graduate students and researchersan introduction to many important topics inmodern algebra within a concrete setting for the former, an exploration of a fascinating subfield of algebraic geometry for the latter
Note:Springer eBooks
Contents:1 First Steps
2 Elements of Algebraic Geometry and Commutative Algebra
3 Applications of Commutative Algebra to Invariant Theory
4 Examples
5 Monomial Orderings and SAGBI Bases
6 Block Bases
7 The Cyclic Group Cp
8 Polynomial Invariant Rings
9 The Transfer
10 Invariant Rings via Localization
11 Rings of Invariants which are Hypersurfaces
12 Separating Invariants
13 Using SAGBI Bases to Compute Rings of Invariants
14 Ladders
References
Index
ISBN:9783642174049
Series:e-books
Series:SpringerLink (Online service)
Series:Encyclopaedia of Mathematical Sciences, 0938-0396 : v139
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Geometry, algebraic
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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-2011-9783642035456:ONLINE Show nearby items on shelf
Title:A Course in Commutative Algebra [electronic resource]
Author(s): Gregor Kemper
Date:2011
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This textbook offers a thorough, modern introduction into commutative algebra. It is intented mainly to serve as a guide for a course of one or two semesters, or for self-study. The carefully selected subject matter concentrateson the concepts and re sults at the center of the field. The book maintains a constant view on the natural geometric context, enabling the reader to gain a deeper understanding of the material. Although it emphasizes theory, threechapters are devoted to computational aspects. M any illustrative examples and exercises enrich the text
Note:Springer eBooks
Contents:Introduction
Part I The Algebra Geometry Lexicon: 1 Hilbert's Nullstellensatz 2 Noetherian and Artinian Rings 3 The Zariski Topology 4 A Summary of the Lexicon
Part II Dimension: 5 Krull Dimension and Transcendence Degree 6 Localization 7 The Principal Ideal Theorem 8 Integral Extensions
Part III Computational Methods: 9 Grbner Bases 10 Fibers and Images of Morphisms Revisited 11 Hilbert Series and Dimension
Part IV Local Rings: 12 Dimension Theory 13 Regular Local Rings 14 Rings of Dimension One
References
Notation
Index
ISBN:9783642035456
Series:e-books
Series:SpringerLink (Online service)
Series:Graduate Texts in Mathematics, 0072-5285 : v256
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Algebra , Computer science Mathematics
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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-2011-9780857291776:ONLINE Show nearby items on shelf
Title:Graded Syzygies [electronic resource]
Author(s): Irena Peeva
Date:2011
Publisher:London : Springer London
Size:1 online resource
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Note:The study of free resolutions is a core and beautiful area in Commutative Algebra. The main goal of this book is to inspire the readers and develop their intuition about syzygies and Hilbert functions. Many examples are given inorder to illustrate id eas and key concepts. A valuable feature of the book is the inclusion of open problems and conjectures these provide a glimpse of exciting, and often challenging, research directions in the field. Three types ofproblems are presented: Conjectures, Problem s, and Open-Ended Problems. The latter do not describe specific problems but point to interesting directions for exploration. The first part of the monograph contains basic backgroundmaterial on graded free resolutions. Further coverage of topics includes syzygies over a polynomial ring, resolutions over quotient rings, lex ideals and Hilbert functions, compression, resolutions of monomial ideals, and syzygies oftoric ideals. With a clear and self-contained exposition this text is intended for advanced gr aduate students and postdoctorates it will be also of interest to senior mathematicians
Note:Springer eBooks
Contents:Graded Free Resolutions
Hilbert Functions
Monomial Resolutions
Syzygies of Toric Ideals
ISBN:9780857291776
Series:e-books
Series:SpringerLink (Online service)
Series:Algebra and Applications : v14
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra
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Call number:SPRINGER-2010-9783642133688:ONLINE Show nearby items on shelf
Title:The Use of Ultraproducts in Commutative Algebra [electronic resource]
Author(s): Hans Schoutens
Date:2010
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
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Note:In spite of some recent applications of ultraproducts in algebra, they remain largely unknown to commutative algebraists, in part because they do not preserve basic properties such as Noetherianity. This work wants to make astrong case against these prejudices. More precisely, it studies ultraproducts of Noetherian local rings from a purely algebraic perspective, as well as how they can be used to transfer results between the positive and zerocharacteristics, to derive uniform bounds, to define tight closure in characteristic zero, and to prove asymptotic versions of homological conjectures in mixed characteristic. Some of these results are obtained using variants calledchromatic products, which are often even Noetherian. This book, neither assuming nor using any logical formalism, is intended for algebraists and geometers, in the hope of popularizing ultraproducts and their applications in algebra
Note:Springer eBooks
Contents:Ultraproducts and ?o? Theorem
Flatness
Uniform Bounds
Tight Closure in Positive Characteristic
Tight Closure in Characteristic Zero. Affine Case
Tight Closure in Characteristic Zero. Local Case
Cataproducts
Protoproducts
Asymptotic Homological Conjectures in Mixed Characteristic
ISBN:9783642133688
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Mathematics, 0075-8434 : v1999
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Algebra
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Call number:SPRINGER-2010-9783034800525:ONLINE Show nearby items on shelf
Title:Simplicial Methods for Operads and Algebraic Geometry [electronic resource]
Author(s): Ieke Moerdijk
Bertrand Ton
Date:2010
Publisher:Basel : Springer Basel
Size:1 online resource
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Note:This book is an introduction to two higher-categorical topics in algebraic topology and algebraic geometry relying on simplicial methods. Moerdijks lectures offer a detailed introduction to dendroidal sets, which wereintroduced by himself and Weiss a s a foundation for the homotopy theory of operads. The theory of dendroidal sets is based on trees instead of linear orders and has many features analogous to the theory of simplicial sets, but it alsoreveals new phenomena. For example, dendroidal sets ad mit a closed symmetric monoidal structure related to the BoardmanVogt tensor product of operads. The lecture notes start with the combinatorics of trees and culminate with asuitable model structure on the category of dendroidal sets. Important concepts ar e illustrated with pictures and examples. The lecture series by Ton presents derived algebraic geometry. While classical algebraic geometry studiesfunctors from the category of commutative rings to the category of sets, derived algebraic geometry is conce rned with functors from simplicial commutative rings (to allow derived tensor products) to simplicial sets (to allow derivedquotients). The central objects are derived (higher) stacks, which are functors satisfying a certain up-to-homotopy descent conditi on. These lectures provide a concise and focused introduction to this vast subject, glossing over manyof the technicalities that make the subjects research literature so overwhelming. Both sets of lectures assume a working knowledge of model categories in the sense of Quillen. For Tons lectures, some background in algebraicgeometry is also necessary
Note:Springer eBooks
ISBN:9783034800525
Series:e-books
Series:SpringerLink (Online service)
Series:Advanced Courses in Mathematics - CRM Barcelona
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Algebraic topology
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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
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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-2009-9781848829411:ONLINE Show nearby items on shelf
Title:Group and Ring Theoretic Properties of Polycyclic Groups [electronic resource]
Author(s): B.A.F Wehrfritz
Date:2009
Publisher:London : Springer London
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Polycyclic groups are built from cyclic groups in a specific way. They arise in many contexts within group theory itself but also more generally in algebra, for example in the theory of Noetherian rings. They also touch on someaspects of topology, ge ometry and number theory. The first half of this book develops the standard group theoretic techniques for studying polycyclic groups and the basic properties of these groups. The second half then focusesspecifically on the ring theoretic properties of po lycyclic groups and their applications, often to purely group theoretic situations. The book is not intended to be encyclopedic. Instead, it is a study manual for graduate students andresearchers coming into contact with polycyclic groups, where the main lines of the subject can be learned from scratch by any reader who has been exposed to some undergraduate algebra, especially groups, rings and vector spaces. Thusthe book has been kept short and readable with a view that it can be read and worked through from cover to cover. At the end of each topic covered there is a description without proofs, but with full references, of further developmentsin the area. The book then concludes with an extensive bibliography of items relating to polycyclic groups
Note:Springer eBooks
Contents:Foreword
Some basic group theory
Some ring theory
Soluble linear groups
Further group
theoretic properties of polycyclic groups
Groups acting on finitely generated commutative rings
Prime ideals in polycyclic
group rings
The structure of modules over polycyclic groups
Semilinear and skew linear groups
ISBN:9781848829411
Series:e-books
Series:SpringerLink (Online service)
Series:Algebra and Applications : v10
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Group theory
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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-2008-9783540735427:ONLINE Show nearby items on shelf
Title:A Singular Introduction to Commutative Algebra [electronic resource]
Author(s): Gert-Martin Greuel
Gerhard Pfister
Date:2008
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
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Note:From the reviews: It is certainly no exaggeration to say that Greuel and Pfister's A Singular Introduction to Commutative Algebra aims to lead a further stage in the computational revolution in commutative algebra, in whichcomputational methods and r esults become central to how the subject is taught and learned. [] Among the great strengths and most distinctive features of Greuel and Pfister's book is a new, completely unified treatment of the globaland local theories. The realization that the two ca ses could be combined to this extent was decisive in the design of the Singular system, making it one of the most flexible and most efficient systems of its type. The authors presentthe first systematic development of this unified approach in a textbook h ere, and this aspect alone is almost worth the price of admission. Another distinctive feature of this book is the degree of integration of explicit computationalexamples into the flow of the text. Strictly mathematical components of the development (ofte n quite terse and written in a formal theorem-proof style) are interspersed with parallel discussions of features of Singular and numerousSingular examples giving input commands, some extended programs in the Singular language, and output. [] Yet another strength of Greuel and Pfister's book is its breadth of coverage of theoretical topics in the portions ofcommutative algebra closest to algebraic geometry, with algorithmic treatments of almost every topic. A synopsis of the table of contents will make th is clear. [] Greuel and Pfister have written a distinctive an highly useful bookthat should be in the library of every commutative algebrais and algebraic geometer, expert and novice alike. I hope that it achieves the educational impact it deserves. John B. Little, Monthly of The Mathematical Association ofAmerica, March 2004 ... The authors' most important new focus is the presentation of non-well orderings that allow them the computat
Note:Springer eBooks
Contents:Rings, Ideals and Standard Bases
Modules
Noether Normalization and Applications
Primary Decomposition and Related Topics
Hilbert Function and Dimension
Complete Local Rings
Homological Algebra
ISBN:9783540735427
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra Data processing , Algebra , Geometry, algebraic , Computer science Mathematics , Algorithms
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Call number:SPRINGER-2008-9781848001855:ONLINE Show nearby items on shelf
Title:Catalan's Conjecture [electronic resource]
Author(s): Ren Schoof
Date:2008
Edition:1
Publisher:London : Springer London : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Eugne Charles Catalan made his famous conjecture that 8 and 9 are the only two consecutive perfect powers of natural numbers in 1844 in a letter to the editor of Crelles mathematical journal. One hundred andfifty-eight years later, Preda Mihailescu proved it. Catalans Conjecture presents this spectacular result in a way that is accessible to the advanced undergraduate. The first few sections of the book require little more than a basicmathematical background and some knowledge of elementary number theory, while later sections involve Galois theory, algebraic number theory and a small amount of commutative algebra. The prerequisites, such as the basic facts from thearithmetic of cyclotomic fields, are all discussed within the text. The author dissec ts both Mihailescus proof and the earlier work it made use of, taking great care to select streamlined and transparent versions of the argumentsand to keep the text self-contained. Only in the proof of Thaines theorem is a little class field theory used i t is hoped that this application will motivate the interested reader to study the theory further. Beautifully clear andconcise, this book will appeal not only to specialists in number theory but to anyone interested in seeing the application of the ideas of algebraic number theory to a famous mathematical problem
Note:Springer eBooks
Contents:The Case q = 2
The Case p = 2
The Nontrivial Solution
Runges Method
Cassels theorem
An Obstruction Group
Small p or q
The Stickelberger Ideal
The Double Wieferich Criterion
The Minus Argument
The Plus Argument I
Semisimple Group Rings
The Plus Argument II
The Density Theorem
Thaines Theorem
ISBN:9781848001855
Series:e-books
Series:SpringerLink (Online service)
Series:Universitext, 0172-5939
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Number theory
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Call number:SPRINGER-2008-9781402069475:ONLINE Show nearby items on shelf
Title:Difference Algebra [electronic resource]
Author(s): Alexander Levin
Date:2008
Publisher:Dordrecht : Springer Netherlands
Size:1 online resource
Note:Springer e-book platform
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Note:Difference algebra grew out of the study of algebraic difference equations with coefficients from functional fields in much the same way as the classical algebraic geometry arose from the study of polynomial equations withnumerical coefficients. The first stage of the development of the theory is associated with its founder J. F. Ritt (1893 - 1951) and R. Cohn whose book Difference Algebra (1965) remained the only fundamental monograph on the subjectfor many years. Nowadays, difference algebra has ov ergrew the frame of the theory of ordinary algebraic difference equations and appears as a rich theory with applications to the study of equations in finite differences, functionalequations, differential equations with delay, algebraic structures with ope rators, group and semigroup rings. This book reflects the contemporary level of difference algebra it contains a systematic study of partial differencealgebraic structures and their applications, as well as the coverage of the classical theory of ordinary difference rings and field extensions. The monograph is intended for graduate students and researchers in difference anddifferential algebra, commutative algebra, ring theory, and algebraic geometry. It will be also of interest to researchers in computer algebra, theory of difference equations and equations of mathematical physics. The book isself-contained it requires no prerequisites other than knowledge of basic algebraic concepts and mathematical maturity of an advanced undergraduate
Note:Springer eBooks
Contents:Preliminaries
Basic Concepts of Difference Algebra
Difference Modules
Difference Field Extensions
Compatibility, Replicability, and Monadicity
Difference Kernels over Partial Difference Fields. Difference Valuation Rings
Systems of Algebraic Difference Equations
Elements of the Difference Galois Theory
ISBN:9781402069475
Series:e-books
Series:SpringerLink (Online service)
Series:Algebra and Applications : v8
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Field theory (Physics) , Functional equations
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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
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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-2006-9780817645298:ONLINE Show nearby items on shelf
Title:Basic Algebra [electronic resource]
Author(s): Anthony W Knapp
Date:2006
Publisher:Boston, MA : Birkhuser Boston
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a globalview of algebra and its r ole in mathematics as a whole. Key topics and features of Basic Algebra: *Linear algebra and group theory build on each other continually *Chapters on modern algebra treat groups, rings, fields, modules, andGalois groups, with emphasis on methods of compu tation throughout *Three prominent themes recur and blend together at times: the analogy between integers and polynomials in one variable over a field, the interplay between linearalgebra and group theory, and the relationship between number theory and ge ometry *Many examples and hundreds of problems are included, along with a separate 90-page section giving hints or complete solutions for most of the problems*The exposition proceeds from the particular to the general, often providing examples well before a theory that incorporates them includes blocks of problems that introduce additional topics and applications for further study*Applications to science and engineering (e.g., the fast Fourier transform, the theory of error-correcting codes, the use of th e Jordan canonical form in solving linear systems of ordinary differential equations, and constructions ofinterest in mathematical physics) appear in sequences of problems Basic Algebra presents the subject matter in a forward-looking way that takes into account its historical development. It is suitable as a text in a two-semesteradvanced undergraduate or first-year graduate sequence in algebra, possibly supplemented by some material from Advanced Algebra at the graduate level. It requires of the reader only familiarity with matrix algebra, an understanding ofthe geometry and reduction of linear equations, and an acquaintance with proofs
Note:Springer eBooks
Contents:Preliminaries about the Integers, Polynomials, and Matrices
Vector Spaces over ?, ?, and ?
Inner
Product Spaces
Groups and Group Actions
Theory of a Single Linear Transformation
Multilinear Algebra
Advanced Group Theory
Commutative Rings and Their Modules
Fields and Galois Theory
Modules over Noncommutative Rings
ISBN:9780817645298
Series:e-books
Series:SpringerLink (Online service)
Series:Cornerstones
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Field theory (Physics) , Group theory , Matrix theory
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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-2005-9783540282969:ONLINE Show nearby items on shelf
Title:Computational Commutative Algebra 2 [electronic resource]
Author(s): Martin Kreuzer
Lorenzo Robbiano
Date:2005
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Computational Commutative Algebra 2 is the natural continuation of Computational Commutative Algebra 1 with some twists, starting with the differently coloured cover graphics. The first volume had 3 chapters, 20 sections, 44tutorials, and some amusin g quotes. Since bigger is better, this book contains 3 chapters filling almost twice as many pages, 23 sections (some as big as a whole chapter), and 55 tutorials (some as big as a whole section). The numberof jokes and quotes has increased exponentially due to the little-known fact that a good mathematical joke is better than a dozen mediocre papers. The main part of this book is a breathtaking passeggiata through the computationaldomains of graded rings and modules and their Hilbert functions. Besides G rbner bases, we encounter Hilbert bases, border bases, SAGBI bases, and even SuperG bases. The tutorials traverse areas ranging from algebraic geometry andcombinatorics to photogrammetry, magic squares, coding theory, statistics, and automatic theorem pro ving. Whereas in the first volume gardening and chess playing were not treated, in this volume they are. This is a book for learning,teaching, reading, and most of all, enjoying the topic at hand. The theories it describes can be applied to anything from children's toys to oil production. If you buy it, probably one spot on your desk will be lost forever!
Note:Springer eBooks
Contents:Foreword
Introduction
The Homogeneous Case
Hilbert Functions
Further Applications
A. The ABC of CoCoA 5
B. Suggestions for Further Reading
C. Hints for Selected Exercises
Bibliography
ISBN:9783540282969
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra Data processing , Algebra , Geometry, algebraic , Algorithms
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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
Note:Springer e-book platform
Note:Springer 2013 e-book collections
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
Note:Springer e-book platform
Note:Springer 2013 e-book collections
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-2002-9783662049631:ONLINE Show nearby items on shelf
Title:A Singular Introduction to Commutative Algebra
Author(s): Gert-Martin Greuel
Date:2002
Size:1 online resource (588 p.)
Note:10.1007/978-3-662-04963-1
Contents:1. Rings, Ideals and Standard Bases -- 1.1 Rings, Polynomials and Ring Maps -- 1.2 Monomial Orderings -- 1.3 Ideals and Quotient Rings -- 1.4 Local Rings and Localization -- 1.5 Rings Associated to Monomial Orderings -- 1.6 Normal
Forms and Standard Bases -- 1.7 The Standard Basis Algorithm -- 1.8 Operations on Ideals and Their Computation -- 2. Modules -- 2.1 Modules, Submodules and Homomorphisms -- 2.2 Graded Rings and Modules -- 2.3 Standard Bases for Modules
-- 2.4 Exact Sequences and free Resolutions -- 2.5 Computing Resolutions and the Syzygy Theorem -- 2.6 Modules over Principal Ideal Domains -- 2.7 Tensor Product -- 2.8 Operations on Modules and Their Computation -- 3. Noether
Normalization and Applications -- 3.1 Finite and Integral Extensions -- 3.2 The Integral Closure -- 3.3 Dimension -- 3.4 Noether Normalization -- 3.5 Applications -- 3.6 An Algorithm to Compute the Normalization -- 3.7 Procedures -- 4.
Primary Decomposition and Related Topics -- 4.1 The Theory of Primary Decomposition -- 4.2 Zero-dimensional Primary Decomposition -- 4.3 Higher Dimensional Primary Decomposition -- 4.4 The Equidimensional Part of an Ideal -- 4.5 The
Radical -- 4.6 Procedures -- 5. Hilbert Function and Dimension -- 5.1 The Hilbert Function and the Hilbert Polynomial -- 5.2 Computation of the Hilbert-Poincaré Series -- 5.3 Properties of the Hilbert Polynomial -- 5.4 Filtrations and
the Lemma of Artin-Rees -- 5.5 The Hilbert-Samuel Function -- 5.6 Characterization of the Dimension of Local Rings -- 5.7 Singular Locus -- 6. Complete Local Rings -- 6.1 Formal Power Series Rings -- 6.2 Weierstraß Preparation Theorem
-- 6.3 Completions -- 6.4 Standard Bases -- 7. Homological Algebra -- 7.1 Tor and Exactness -- 7.2 Fitting Ideals -- 7.3 Flatness -- 7.4 Local Criteria for Flatness -- 7.5 Flatness and Standard Bases -- 7.6 Koszul Complex and Depth --
7.7 Cohen-Macaulay Rings -- 7.8 Further Characterization of Cohen-Macaulayness -- 7.9 Homological Characterization of Regular Rings -- A. Geometric Background -- A.1 Introduction by Pictures -- A.2 Affine Algebraic Varieties -- A.3
Spectrum and Affine Schemes -- A.4 Projective Varieties -- A.5 Projective Schemes and Varieties -- A.6 Morphisms Between Varieties -- A.7 Projective Morphisms and Elimination -- A.8 Local Versus Global Properties -- A.9 Singularities
-- B. SINGULAR — A Short Introduction -- B.1 Downloading Instructions -- B.2 Getting Started -- B.3 Procedures and Libraries -- B.4 Data Types -- B.5 Functions -- B.6 Control Structures -- B.7 System Variables -- B.8 Libraries --
References -- Algorithms
ISBN:9783662049631
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Computer science , Algebra , Algebraic geometry , Computer mathematics , Algorithms , Mathematics , Algebra , Algebraic Geometry , Algorithms , Computational Mathematics and Numerical Analysis , Symbolic and Algebraic Manipulation
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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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