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SPIRES-BOOKS: FIND KEYWORD RINGS ALGEBRA *END*INIT* use /tmp/qspiwww.webspi1/6334.119 QRY 131.225.70.96 . find keyword "rings algebra" ( 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-2016-9783034809528:ONLINE Show nearby items on shelf
Title:Module Theory, Extending Modules and Generalizations
Author(s): Adnan Tercan
Date:2016
Size:1 online resource (369 p.)
Note:10.1007/978-3-0348-0952-8
Contents:Preface -- Introduction -- List of Symbols -- Introducing modules -- Types of Relative Injectivity -- Extending Property and Related Concepts -- Inner Generalizations of Extending Modules -- Outer Generalizations of Extending Modules -- Dual Goldie and EC-complement Versions of the Extending Property -- Open Problems and Questions -- Appendix -- References -- Index
ISBN:9783034809528
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Associative rings , Rings (Algebra) , Mathematics , Associative Rings and Algebras
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Call number:SPRINGER-2014-9788876425011:ONLINE Show nearby items on shelf
Title:Introductory Notes on Valuation Rings and Function Fields in One Variable [electronic resource]
Author(s): Renata Scognamillo
Umberto Zannier
Date:2014
Publisher:Pisa : Scuola Normale Superiore : Imprint: Edizioni della Normale
Size:1 online resource
Note:The book deals with the (elementary and introductory) theory of valuation rings. As explained in the introduction, this represents a useful and important viewpoint in algebraic geometry, especially concerning the theory ofalgebraic curves and their f unction fields. The correspondences of this with other viewpoints (e.g. of geometrical or topological nature) are often indicated, also to provide motivations and intuition for many results. Links witharithmetic are also often indicated. There are three a ppendices, concerning Hilberts Nullstellensatz (for which several proofs are provided), Puiseux series and Dedekind domains. There are also several exercises, often accompaniedby hints, which sometimes develop further results not included in full for brev ity reasons
Contents:Generalities on function fields of one variable
Valuation rings
Completions
Appendices on Hilbert's Nullstellensatz, Puiseux series, Dedekind domains
ISBN:9788876425011
Series:eBooks
Series:SpringerLink
Series:Publications of the Scuola Normale Superiore : v14
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Geometry , Number theory
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Call number:SPRINGER-2014-9788132215998:ONLINE Show nearby items on shelf
Title:Basic Modern Algebra with Applications [electronic resource]
Author(s): Mahima Ranjan Adhikari
Avishek Adhikari
Date:2014
Publisher:New Delhi : Springer India : Imprint: Springer
Size:1 online resource
Note:The book is primarily intended as a textbook on modern algebra for undergraduate mathematics students. It is also useful for those who are interested in supplementary reading at a higher level. The text is designed in such a waythat it encourages ind ependent thinking and motivates students towards further study. The book covers all major topics in group, ring, vector space and module theory that are usually contained in a standard modern algebra text. Inaddition, it studies semigroup, group action, Hopf's group, topological groups and Lie groups with their actions, applications of ring theory to algebraic geometry, and defines Zariski topology, as well as applications of module theoryto structure theory of rings and homological algebra. Algebraic as pects of classical number theory and algebraic number theory are also discussed with an eye to developing modern cryptography. Topics on applications to algebraictopology, category theory, algebraic geometry, algebraic number theory, cryptography and theo retical computer science interlink the subject with different areas. Each chapter discusses individual topics, starting from the basics, withthe help of illustrative examples. This comprehensive text with a broad variety of concepts, applications, example s, exercises and historical notes represents a valuable and unique resource
Contents:Prerequisites: Basics of Set Theory and Integers
Groups: Introductory Concepts
Actions of Groups, Topological Groups and semigroups
Rings: Introductory Concepts
Ideals of Rings: Introductory concepts
Factorization in Integral Domains and in Polynomial Rings
Rings with Chain Conditions
Vector Spaces
Modules
Algebraic Aspects of Number Theory
Algebraic Numbers
Introduction to Mathematical Cryptography
Appendix A: Some Aspects of Semirings
Appendix B: Category Theory
Appendix C: A Brief Historical Note
ISBN:9788132215998
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Group theory , Number theory
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Call number:SPRINGER-2014-9783662442050:ONLINE Show nearby items on shelf
Title:Proofs from THE BOOK [electronic resource]
Author(s): Martin Aigner
Gnter M Ziegler
Date:2014
Edition:5th ed. 2014
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:This revised and enlarged fifth editionfeatures four new chapters, which contain highly original and delightful proofs for classics such as the spectral theorem from linear algebra, some more recent jewels like thenon-existence of the Borromean rings and other surprises. From the Reviews ... Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing andglorious ways. There is vast wealth within its pages, one gem aft er another. ... Aigner and Ziegler... write: ... all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliantideas, clever insights and wonderful observations. I do. ... Notices of the AMS, August 1999 ... This book is a pleasure to hold and to look at: ample margins, nice photos, instructive pictures, and beautiful drawings ... It isa pleasure to read as well: the style is clear and entertaining, the level is close to elementary, the necessary bac kground is given separately, and the proofs are brilliant. ... LMS Newsletter, January 1999 Martin Aigner andGnter Ziegler succeeded admirably in putting together a broad collection of theorems and their proofs that would undoubtedly be in the Book of Erd s. The theorems are so fundamental, their proofs so elegant, and the remaining openquestions so intriguing that every mathematician, regardless of speciality, can benefit from reading this book. ... SIGACT News, December 2011
Contents:Number Theory: 1. Six proofs of the infinity of primes
2. Bertrands postulate
3. Binomial coefficients are (almost) never powers
4. Representing numbers as sums of two squares
5. The law of quadratic reciprocity
6. Every finite division ring is a field
7. The spectral theorem and Hadamards determinant problem
8. Some irrational numbers
9. Three times 2/6
Geometry: 10. Hilberts third problem: decomposing polyhedral
11. Lines in the plane and decompositions of graphs
12. The slope problem
13. Three applications of Eulers formula
14. Cauchys
ISBN:9783662442050
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Computer science , Global analysis (Mathematics) , Combinatorics , Geometry , Number theory
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Call number:SPRINGER-2014-9783642412691:ONLINE Show nearby items on shelf
Title:Some Topics in Algebra [electronic resource] : An Advanced Undergraduate Course at PKU
Author(s): Michel Brou
Date:2014
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:During the springs of 2011 and 2012, the author was invited by Peking University to give an advanced undergraduate algebra course (once a week over two months each year). This book was written during and for that course. By noway does it claim to be to exhaustive. It was originally intended as a brief introduction to algebra for an extremely pleasant and passionate audience. It certainly reflects some of the authors own tastes, and it was influenced bythe feelings and the reactions of the students. N evertheless, the result covers some advanced undergraduate algebra (rings, ideals, basics of fields theory, algebraic integers, modules, hom and tensor functors, projective modules,etc) illustrated by numerous examples, counterexamples and exercises. Foll owing a worldwide tradition, the author had planned to conclude by lecturing on the structure of finitely generated modules over principal ideal domains. Butduring the course, after explaining that the notion of projective modules is more natural than the notion of free modules, it became clear that principal ideal domains needed to be replaced by Dedekind rings this is much lesstraditional in the literature but not more difficult
Contents:Preface
Rings and polynomial algebras
Modules
ISBN:9783642412691
Series:eBooks
Series:SpringerLink
Series:Mathematical Lectures from Peking University, 2197-4209
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra
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Call number:SPRINGER-2014-9783319079684:ONLINE Show nearby items on shelf
Title:Representation Theory [electronic resource] : A Homological Algebra Point of View
Author(s): Alexander Zimmermann
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:Introducing the representation theory of groups and finite dimensional algebras, this book first studies basic non-commutative ring theory, covering the necessary background of elementary homological algebra andrepresentations of groups to block the ory. It further discusses vertices, defect groups, Green and Brauer correspondences and Clifford theory. Whenever possible the statements are presented in a general setting for more generalalgebras, such as symmetric finite dimensional algebras over a fie ld. Then, abelian and derived categories are introduced in detail and are used to explain stable module categories, as well as derived categories and their maininvariants and links between them. Group theoretical applications of these theories are given such as the structure of blocks of cyclic defect groups whenever appropriate. Overall, many methods from the representation theory ofalgebras are introduced. Representation Theory assumes only the most basic knowledge of linear algebra, groups, rings and fields, and guides the reader in the use of categorical equivalences in the representation theory of groups andalgebras. As the book is based on lectures, it will be accessible to any graduate student in algebra and can be used for self-study as well as for classroom use
Contents:Rings, Algebras and Modules
Modular Representations of Finite Groups
Abelian and Triangulated Categories
Morita theory
Stable Module Categories
Derived Equivalences
ISBN:9783319079684
Series:eBooks
Series:SpringerLink
Series:Algebra and Applications, 1572-5553 : v19
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Group theory
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Call number:SPRINGER-2014-9783319064130:ONLINE Show nearby items on shelf
Title:Lattice Theory: Special Topics and Applications [electronic resource] : Volume 1
Author(s): George Grtzer
Friedrich Wehrung
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Birkhuser
Size:1 online resource
Note:George Grtzer's Lattice Theory: Foundation is his third book on lattice theory (General Lattice Theory, 1978, second edition, 1998). In 2009, Grtzer considered updating the second edition to reflect some exciting and deepdevelopments. He soon realize d that to lay the foundation, to survey the contemporary field, to pose research problems, would require more than one volume and more than one person. So Lattice Theory: Foundation provided the foundation.Now we complete this project with Lattice Theory: Special Topics and Applications, written by a distinguished group of experts, to cover some of the vast areas not in Foundation. This first volume is divided into three parts. Part I.Topology and Lattices includes two chapters by Klaus Keimel, Jimmie Law son and Ales Pultr, Jiri Sichler. Part II. Special Classes of Finite Lattices comprises four chapters by Gabor Czedli, George Grtzer and Joseph P. S. Kung. PartIII. Congruence Lattices of Infinite Lattices and Beyond includes four chapters by Friedrich We hrung and George Grtzer
Contents:Introduction. Part I Topology and Lattices
Chapter 1. Continuous and Completely Distributive Lattices
Chapter 2. Frames: Topology Without Points
Part II. Special Classes of Finite Lattices
Chapter 3. Planar Semi modular Lattices: Structure and Diagram
Chapter 4. Planar Semi modular Lattices: Congruences
Chapter 5. Sectionally Complemented Lattices
Chapter 6. Combinatorics in finite lattices
Part III. Congruence Lattices of Infinite Lattices and Beyond
Chapter 7. Schmidt and Pudlk's Approaches to CLP
Chapter 8. Congruences of lattices and ideals of rings
Chapt
ISBN:9783319064130
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra
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Call number:SPRINGER-2014-9783319056487:ONLINE Show nearby items on shelf
Title:Spectral Mapping Theorems [electronic resource] : A Bluffer's Guide
Author(s): Robin Harte
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:Written by an author who was at the forefront of developments in multi-variable spectral theory during the seventies and the eighties, this guide sets out to describe in detail the spectral mapping theorem in one, several andmany variables. The basic algebraic systems semigroups, rings and linear algebras are summarised, and then topological-algebraic systems, including Banach algebras, to set up the basic language of algebra and analysis. SpectralMapping Theorems is written in an easy-to-read and engaging manner and will be useful for both the beginner and expert. It will be of great importance to researchers and postgraduates studying spectral theory
Contents:Algebra
Topology
Topological algebra
Spectral theory
Several variables
Many Variables
ISBN:9783319056487
Series:eBooks
Series:SpringerLink
Series:SpringerBriefs in Mathematics, 2191-8198
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Operator theory
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Call number:SPRINGER-2014-9783319044989:ONLINE Show nearby items on shelf
Title:Abstract Algebra [electronic resource] : Structure and Application
Author(s): David R Finston
Patrick J Morandi
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Birkhuser
Size:1 online resource
Note:This text seeks to generate interest in abstract algebra by introducing each new structure and topic via a real-world application. The down-to-earth presentation is accessible to a readership with no prior knowledge of abstractalgebra. Students are l ed to algebraic concepts and questions in a natural way through their everyday experiences. Applications include: Identification numbers and modular arithmetic (linear) error-correcting codes, including cycliccodes ruler and compass constructions cryptogr aphy symmetry of patterns in the real plane Abstract Algebra: Structure and Application is suitable as a text for a first course on abstract algebra whose main purpose is to generateinterest in the subject, or as a supplementary text for more advanced cou rses. The material paves the way to subsequent courses that further develop the theory of abstract algebra and will appeal to students of mathematics, mathematicseducation, computer science, and engineering interested in applications of algebraic concepts
Contents:Identification Numbers and Modular Arithmetic
Error Correcting Codes
Rings and Fields
Linear Algebra and Linear Codes
Quotient Rings and Field Extensions
Ruler and Compass Constructions
Cyclic Codes
Groups and Cryptography
The Structure of Groups
Symmetry
ISBN:9783319044989
Series:eBooks
Series:SpringerLink
Series:Springer Undergraduate Texts in Mathematics and Technology, 1867-5506
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Matrix theory
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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-2013-9783642309946:ONLINE Show nearby items on shelf
Title:Linear Algebra and Geometry [electronic resource]
Author(s): Igor R Shafarevich
Alexey O Remizov
Date:2013
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This book on linear algebra and geometry is based on a course given by renowned academician I.R. Shafarevich at Moscow State University. The book begins with the theory of linear algebraic equations and the basic elements ofmatrix theory and continue s with vector spaces, linear transformations, inner product spaces, and the theory of affine and projective spaces. The book also includes some subjects that are naturally related to linear algebra but areusually not covered in such courses: exterior alge bras, non-Euclidean geometry, topological properties of projective spaces, theory of quadrics (in affine and projective spaces), decomposition of finite abelian groups, and finitelygenerated periodic modules (similar to Jordan normal forms of linear opera tors). Mathematical reasoning, theorems, and concepts are illustrated with numerous examples from various fields of mathematics, including differential equationsand differential geometry, as well as from mechanics and physics
Note:Springer eBooks
Contents:Preface
Preliminaries
1. Linear Equations
2. Matrices and Determinants
3. Vector Spaces
4. Linear Transformations of a Vector Space to Itself
5. Jordan Normal Form
6. Quadratic and Bilinear Forms
7. Euclidean Spaces
8. Affine Spaces
9. Projective Spaces
10. The Exterior Product and Exterior Algebras
11. Quadrics
12. Hyperbolic Geometry
13. Groups, Rings, and Modules
14. Elements of Representation Theory
Historical Note
References
Index
ISBN:9783642309946
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Matrix theory , Geometry
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Call number:SPRINGER-2013-9783319002576:ONLINE Show nearby items on shelf
Title:The Classification of the Virtually Cyclic Subgroups of the Sphere Braid Groups [electronic resource]
Author(s): Daciberg Lima Goncalves
John Guaschi
Date:2013
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
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Note:This manuscript is devoted to classifying the isomorphism classes of the virtually cyclic subgroups of the braid groups of the 2-sphere. As well as enabling us to understand better the global structure of these groups, it marks animportant step in th e computation of the K-theory of their group rings. The classification itself is somewhat intricate, due to the rich structure of the finite subgroups of these braid groups, and is achieved by an in-depth analysisof their group-theoretical and topological properties, such as their centralisers, normalisers and cohomological periodicity. Another important aspect of our work is the close relationship of the braid groups with mapping class groups.This manuscript will serve as a reference for the study of bra id groups of low-genus surfaces, and isaddressed to graduate students and researchers in low-dimensional, geometric and algebraic topology and in algebra
Note:Springer eBooks
Contents:Introduction and statement of the main results
Virtually cyclic groups: generalities, reduction and the mapping class group
Realisation of the elements of V1(n) and V2(n) in Bn(S2)
Appendix: The subgroups of the binary polyhedral groups
References.
ISBN:9783319002576
Series:e-books
Series:SpringerLink (Online service)
Series:SpringerBriefs in Mathematics, 2191-8198
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Group theory , Algebraic topology
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Call number:SPRINGER-2013-9783034806183:ONLINE Show nearby items on shelf
Title:Elliptic Curves, Hilbert Modular Forms and Galois Deformations [electronic resource]
Author(s): Laurent Berger
Gebhard Bckle
Lassina Dembl
Mladen Dimitrov
Tim Dokchitser
John Voight
Date:2013
Publisher:Basel : Springer Basel : Imprint: Birkhuser
Size:1 online resource
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Note:The notes in this volume correspond to advanced courses given at the Centre de Recerca Matemtica (Bellaterra, Barcelona, Spain) as part of the Research Programme in Arithmetic Geometry in the 2009-2010 academic year. They arenow available in printed form due to the many requests received by the organizers to make the content of the courses publicly available. The material covers the theory of p-adic Galois representations and Fontaine rings, Galoisdeformation theory, arithmetic and computational aspe cts of Hilbert modular forms, and the parity conjecture for elliptic curves
Note:Springer eBooks
Contents:Part I: Galois Deformations
On p
adic Galois Representations
Deformations of Galois Representations
Part II: Hilbert Modular Forms
Arithmetic Aspects of Hilbert Modular Forms and Varieties
Explicit Methods for Hilbert Modular Forms
Part III: Elliptic Curves
Notes on the Parity Conjecture
ISBN:9783034806183
Series:e-books
Series:SpringerLink (Online service)
Series:Advanced Courses in Mathematics - CRM Barcelona
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Geometry, algebraic , Number theory
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Call number:SPRINGER-2013-9781461466574:ONLINE Show nearby items on shelf
Title:Elliptic Curves and Arithmetic Invariants [electronic resource]
Author(s): Haruzo Hida
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
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Note:This book contains a detailed account of the result of the author's recent Annals paper and JAMS paper on arithmetic invariant, including -invariant, L-invariant, and similar topics. This book can be regarded as anintroductory text to the author's pr evious book p-Adic Automorphic Forms on Shimura Varieties. Written as a down-to-earth introduction to Shimura varieties, this text includes many examples and applications of the theory that providemotivation for the reader. Since it is limited to modular curves and the corresponding Shimura varieties, this book is not only a great resource for experts in the field, but it is also accessible to advanced graduate studentsstudying number theory. Key topics include non-triviality of arithmetic invariants and special values of L-functions elliptic curves over complex and p-adic fields Hecke algebras scheme theory elliptic and modular curves overrings and Shimura curves
Note:Springer eBooks
Contents:1 Non
triviality of Arithmetic Invariants
2Elliptic Curves and Modular Forms
3Invariants, Shimura Variety and Hecke Algebra
4Review of Scheme Theory
5Geometry of Variety
6 Elliptic and Modular Curves over Rings
7Modular Curves as Shimura Variety
8Non
vanishing Modulo p of Hecke Lvalues
9p
Adic Hecke L
functions and their
invariants
10Toric Subschemes in a Split Formal Torus
11Hecke Stable Subvariety is a Shimura Subvariety
References
Symbol Index
Statement Index
Subject Index
ISBN:9781461466574
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Monographs in Mathematics, 1439-7382
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Number theory
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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
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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-2013-9781461436317:ONLINE Show nearby items on shelf
Title:A Logical Introduction to Proof [electronic resource]
Author(s): Daniel W Cunningham
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
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Note:A Logical Introduction to Proof is a unique textbook that uses a logic-first approach to train and guide undergraduates through a transition or bridge course between calculus and advanced mathematics courses. Theauthors approach prepares the student for the rigors required in future mathematics courses and is appropriate for majors in mathematics, computer science, engineering, as well as other applied mathematical sciences. It may alsobe beneficial as a supplement for students at the graduate level who need guidance or reference for writing proofs. Core topics covered are logic, sets, relations, functions, and induction, where logic is the instrument foranalyzing the structure of mathematical assertions and is a tool for composing mathematical proof s. Exercises are given at the end of each section within a chapter. Chapter 1 focuses on propositional logic while Chapter 2 is devoted tothe logic of quantifiers. Chapter 3 methodically presents the key strategies that are used in mathematical proofs eac h presented as a proof diagram. Every proof strategy is carefully illustrated by a variety of mathematical theoremsconcerning the natural, rational, and real numbers. Chapter 4 focuses on mathematical induction and concludes with a proof of the fundamenta l theorem of arithmetic. Chapters 5 through 7 introduce students to the essential concepts thatappear in all branches of mathematics. Chapter 8 introduces the basic structures of abstract algebra: groups, rings, quotient groups, and quotient rings. Finall y, Chapter 9 presents proof strategies that explicitly show students how todeal with the fundamental definitions that they will encounter in real analysis, followed by numerous examples of proofs that use these strategies. The appendix provides a useful s ummary of strategies for dealing with proofs
Note:Springer eBooks
Contents:Preface
The Greek Alphabet
1. Propositional Logic
2. Predicate Logic
3. Proof Strategies and Diagrams
4. Mathematical Induction
5. Set Theory
6. Functions
7. Relations
8. Core Concepts in Abstract Algebra
9. Core Concepts in Real Analysis
A Summary of Strategies
References
List of Symbols. Index
ISBN:9781461436317
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Logic, Symbolic and mathematical
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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
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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-2013-9780387927169:ONLINE Show nearby items on shelf
Title:Extensions of Rings and Modules [electronic resource]
Author(s): Gary F Birkenmeier
Jae Keol Park
S Tariq Rizvi
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
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Note:The focus of this monograph is the study of rings and modules which have a rich supply of direct summands with respect to various extensions. The first four chapters of the book discuss rings and modules which generalizeinjectivity (e.g., extending m odules), or for which certain annihilators become direct summands (e.g., Baer rings). Ring extensions such as matrix, polynomial, group ring, and essential extensions of rings from the aforementionedclasses are considered in the next three chapters. A the ory of ring and module hulls relative to a specific class of rings or modules is introduced and developed in the following two chapters. While applications of the resultspresented can be found throughout the book, the final chapter mainly consists of appl ications to algebra and functional analysis. These include obtaining characterizations of rings of quotients as direct products of prime rings anddescriptions of certain C*-algebras via (quasi-)Baer rings. Extensions of Rings and Modules introduces for th e first time in book form: * Baer, quasi-Baer, and Rickart modules * The theory of generalized triangular matrix rings viasets of triangulating idempotents * A discussion of essential overrings that are not rings of quotients of a base ring and Osofsky's study on the self-injectivity of the injective hull of a ring * Applications of the theory ofquasi-Baer rings to C*-algebras Each section of the book is enriched with examples and exercises which make this monograph useful not only for experts but also as a text for advanced graduate courses. Historical notes appear at the endof each chapter, and a list of Open Problems and Questions is provided to stimulate further research in this area. With over 400 references, Extensions of Rings and Modules will be o f interest to researchers in algebra and analysis andto advanced graduate students in mathematics
Note:Springer eBooks
Contents:Preliminaries and Basic Results
Injectivity and Some of Its Generalizations
Baer, Rickart, and Quasi
Baer Rings
Baer, Quasi
Baer Modules, and Their Applications
Triangular Matrix Representations and Triangular Matrix Extensions
Matrix, Polynomial, and Group Ring Extensions
Essential Overring Extensions
Beyond the Maximal Ring of Quotients
Ring and Module Hulls
Hulls of Ring Extensions
Applications to Rings of Quotients and C* Algebras
Open Problems and Questions
References
Index
ISBN:9780387927169
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Matrix theory , Functional analysis
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Call number:SPRINGER-2012-9783642311529:ONLINE Show nearby items on shelf
Title:Prime Divisors and Noncommutative Valuation Theory [electronic resource]
Author(s): Hidetoshi Marubayashi
Fred Van Oystaeyen
Date:2012
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
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Note:Classical valuation theory has applications in number theory and class field theory as well as in algebraic geometry, e.g. in a divisor theory for curves. But the noncommutative equivalent is mainly applied to finitedimensional skewfields. Recently h owever, new types of algebras have become popular in modern algebra Weyl algebras, deformed and quantized algebras, quantum groups and Hopf algebras, etc. The advantage of valuation theory in thecommutative case is that it allows effective calculations, b ringing the arithmetical properties of the ground field into the picture. This arithmetical nature is also present in the theory of maximal orders in central simplealgebras. Firstly, we aim at uniting maximal orders, valuation rings, Dubrovin valuations, etc. in a common theory, the theory of primes of algebras. Secondly, we establish possible applications of the noncommutative arithmetics tointeresting classes of algebras, including the extension of central valuations to nice classes of quantized algebra s, the development of a theory of Hopf valuations on Hopf algebras and quantum groups, noncommutative valuations on theWeyl field and interesting rings of invariants and valuations of Gauss extensions
Note:Springer eBooks
Contents:1. General Theory of Primes
2. Maximal Orders and Primes
3. Extensions of Valuations to some Quantized Algebras
ISBN:9783642311529
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Mathematics, 0075-8434 : v2059
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Geometry, algebraic , Geometry
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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
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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-2012-9781461412311:ONLINE Show nearby items on shelf
Title:Representing Finite Groups [electronic resource] : A Semisimple Introduction
Author(s): Ambar N Sengupta
Date:2012
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
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Note:This graduate textbook presents the basics of representation theory for finite groups from the point of view of semisimple algebras and modules over them. The presentation interweaves insights from specific examples withdevelopment of general and pow erful tools based on the notion of semisimplicity. The elegant ideas of commutant duality are introduced, along with an introduction to representations of unitary groups.The text progressessystematically and the presentation is friendly and inviting. Cent ral concepts are revisited and exploredfrom multiple viewpoints. Exercises at the end of the chapter help reinforce the material. Representing Finite Groups: ASemisimple Introduction would serve as a textbook for graduate and some advanced undergraduate c ourses in mathematics. Prerequisites include acquaintance with elementary group theory and some familiarity with rings and modules. A finalchapter presents a self-contained account of notions and results in algebra that are used. Researchers in mathematic s and mathematical physics will also find this book useful. A separate solutions manual is available for instructors
Note:Springer eBooks
ISBN:9781461412311
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Group theory , Quantum 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
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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-2012-9781447122944:ONLINE Show nearby items on shelf
Title:Syzygies and Homotopy Theory [electronic resource]
Author(s): F.E.A Johnson
Date:2012
Publisher:London : Springer London
Size:1 online resource
Note:Springer e-book platform
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Note:The most important invariant of a topological space is its fundamental group. When this is trivial, the resulting homotopy theory is well researched and familiar. In the general case, however, homotopy theory over nontrivialfundamental groups is much more problematic and far less well understood. Syzygies and Homotopy Theory explores the problem of nonsimply connected homotopy in the first nontrivial cases and presents, for the first time, a systematicrehabilitation of Hilbert's method of syzygies in the context of non-simply connected homotopy theory. The first part of the book is theoretical, formulated to allow a general finitely presented group as a fundamental group. Theinnovation here is to regard syzygies as stable modules rather than minimal modules. Inevitably this forces a reconsideration of the problems of noncancellation these are confronted in the second, practical, part of the book. Inparticular, the second part of the book considers how the theory works out in detail for the specific e xamples Fn F where Fn is a free group of rank n and F is finite. Another innovation is to parametrize the first syzygy in terms ofthe more familiar class of stably free modules. Furthermore, detailed description of these stably free modules is effected by a suitable modification of the method of Milnor squares. The theory developed within this book has potentialapplications in various branches of algebra, including homological algebra, ring theory and K-theory. Syzygies and Homotopy Theory will be of inte rest to researchers and also to graduate students with a background in algebra andalgebraic topology
Note:Springer eBooks
Contents:Preliminaries
The restricted linear group
The calculus of corners and squares
Extensions of modules
The derived module category
Finiteness conditions
The Swan mapping
Classification of algebraic complexes
Rings with stably free cancellation
Group rings of cyclic groups
Group rings of dihedral groups
Group rings of quaternionic groups
Parametrizing W1 (Z) : generic case
Parametrizing W1 (Z) : singular case
Generalized Swan modules
Parametrizing W1 (Z) : G = C F
Conclusion
ISBN:9781447122944
Series:e-books
Series:SpringerLink (Online service)
Series:Algebra and Applications, 1572-5553 : v17
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Group theory
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Call number:SPRINGER-2012-9780817646424:ONLINE Show nearby items on shelf
Title:Sheaves of Algebras over Boolean Spaces [electronic resource]
Author(s): Arthur Knoebel
Date:2012
Publisher:Boston, MA : Birkhuser Boston : Imprint: Birkhuser
Size:1 online resource
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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-2011-9783642217746:ONLINE Show nearby items on shelf
Title:From Objects to Diagrams for Ranges of Functors [electronic resource]
Author(s): Pierre Gillibert
Friedrich Wehrung
Date:2011
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
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Note:This work introduces tools from the field of category theory that make it possible to tackle a number of representation problems that have remained unsolvable to date (e.g. the determination of the range of a given functor). Thebasic idea is: if a fu nctor lifts many objects, then it also lifts many (poset-indexed) diagrams
Note:Springer eBooks
Contents:1 Background
2 Boolean Algebras Scaled with Respect to a Poset
3 The Condensate Lifting Lemma (CLL)
4 Larders from First
order Structures
5 Congruence
Preserving Extensions
6 Larders from von Neumann Regular Rings
7 Discussion
ISBN:9783642217746
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Mathematics, 0075-8434 : v2029
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , K-theory , Logic, Symbolic and mathematical
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Call number:SPRINGER-2011-9783642211478:ONLINE Show nearby items on shelf
Title:p-Adic Lie Groups [electronic resource]
Author(s): Peter Schneider
Date:2011
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
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Note:Manifolds over complete nonarchimedean fields together with notions like tangent spaces and vector fields form a convenient geometric language to express the basic formalism of p-adic analysis. The volume starts with aself-contained and detailed intr oduction to this language. This includes the discussion of spaces of locally analytic functions as topological vector spaces, important for applications in representation theory. The author then sets upthe analytic foundations of the theory of p-adic Lie groups and develops the relation between p-adic Lie groups and their Lie algebras. The second part of the book contains, for the first time in a textbook, a detailed exposition ofLazard's algebraic approach to compact p-adic Lie groups, via his notion of a p-valuation, together with its application to the structure of completed group rings
Note:Springer eBooks
Contents:Introduction
Part A: p
Adic Analysis and Lie Groups
I.Foundations
I.1.Ultrametric Spaces
I.2.Nonarchimedean Fields
I.3.Convergent Series
I.4.Differentiability
I.5.Power Series
I.6.Locally Analytic Functions
II.Manifolds
II.7.Charts and Atlases
II.8.Manifolds
II.9.The Tangent Space
II.10.The Topological Vector Space C^an(M,E), part 1
II.11 Locally Convex K
Vector Spaces
II.12 The Topological Vector Space C^an(M,E), part 2
III.Lie Groups
III.13.Definitions and Foundations
III.14.The Universal Enveloping Algebra
III.15.The Concept of Free
ISBN:9783642211478
Series:e-books
Series:SpringerLink (Online service)
Series:Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 0072-7830 : v344
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Topological Groups
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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
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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-2011-9783642151286:ONLINE Show nearby items on shelf
Title:Algebraic Patching [electronic resource]
Author(s): Moshe Jarden
Date:2011
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Assuming only basic algebra and Galois theory, the book develops the method of algebraic patching to realize finite groups and, more generally, to solve finite split embedding problems over fields. The method succeeds overrational function fields of one variable over ample fields. Among others, it leads to the solution of two central results in Field Arithmetic: (a) The absolute Galois group of a countable Hilbertian pac field is free oncountably many generators (b) The absolute Galois group of a fun ction field of one variable over an algebraically closed field $C$ is free of rank equal to the cardinality of $C$
Note:Springer eBooks
Contents:1. Algebraic Patching
2. Normed Rings
3. Several Variables
4. Constant Split Embedding Problems over Complete Fields
5. Ample Fields
6. Non
Ample Fields
7. Split Embedding Problems over Complete Fields
8. Split Embedding Problems over Ample Fields
9. The Absolute Galois Group of C(t)
10. Semi
Free Profinite Groups
11. Function Fields of One Variable over PAC Fields
12. Complete Noetherian Domains
Open Problems
References
Glossary of Notation
Index
ISBN:9783642151286
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Monographs in Mathematics, 1439-7382
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Field theory (Physics) , Group theory
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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
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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
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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-2011-9780857298508:ONLINE Show nearby items on shelf
Title:On Normalized Integral Table Algebras (Fusion Rings) [electronic resource] : Generated by a Faithful Non-real Element of Degree 3
Author(s): Zvi Arad
Xu Bangteng
Guiyun Chen
Effi Cohen
Arisha Haj Ihia Hussam
Mikhail Muzychuk
Date:2011
Publisher:London : Springer London : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Springer eBooks
ISBN:9780857298508
Series:e-books
Series:SpringerLink (Online service)
Series:Algebra and Applications, 1572-5553 : v16
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Group theory , Combinatorics
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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
Note:Springer e-book platform
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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-2011-9780387727660:ONLINE Show nearby items on shelf
Title:An Introduction to Hopf Algebras [electronic resource]
Author(s): Robert G Underwood
Date:2011
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
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Note:The study of Hopf algebras spans many fields in mathematics including topology, algebraic geometry, algebraic number theory, Galois moduletheory, cohomology of groups, and formal groups and has wide-ranging connections tofields from theoretical physi cs to computer science. This text is unique in making this engaging subject accessible toadvanced graduate and beginning graduate students and focuses on applications of Hopf algebras to algebraic numbertheory and Galois module theory, providing a smooth transition from modern algebra toHopf algebras. After providing an introduction to the spectrum of a ring and the Zariski topology, the text treats presheaves, sheaves, andrepresentable group functors. In this way the student transitions smoothly from bas ic algebraic geometry to Hopf algebras. The importance of Hopf orders is underscored with applications to algebraic number theory, Galois moduletheory and the theory of formal groups. By the end of the book, readers will be familiar with established resul ts in the field and ready to pose research questions of their own. An exercise set is included in each of twelve chapterswith questionsranging in difficulty. Open problems and research questions arepresented in the last chapter. Prerequisites include an u nderstanding of the material on groups, rings, and fields normally covered in abasic coursein modern algebra
Note:Springer eBooks
Contents:Preface
Some Notation
1. The Spectrum of a Ring
2. The Zariski Topology on the Spectrum
3. Representable Group Functors
4. Hopf Algebras
5. Larson Orders
6. Formal Group Hopf Orders
7. Hopf Orders in KC_p
8. Hopf Orders in KC_{p^2}
9. Hopf Orders in KC_{p^3}
10. Hopf Orders and Galois Module Theory
11. The Class Group of a Hopf Order
12. Open Questions and Research Problems
Bibliography
Index
ISBN:9780387727660
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-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:Springer 2013 e-book collections
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
Note:Springer e-book platform
Note:Springer 2013 e-book collections
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-2010-9783034602860:ONLINE Show nearby items on shelf
Title:Advances in Ring Theory [electronic resource]
Author(s): Dinh Huynh
Sergio R Lpez-Permouth
Date:2010
Publisher:Basel : Birkhuser Basel
Size:1 online resource
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Note:This volume consists of refereed research and expository articles by both plenary and other speakers at the International Conference on Algebra and Applications held at Ohio University in June 2008, to honor S.K. Jain on his 70thbirthday. The article s are on a wide variety of areas in classical ring theory and module theory, such as rings satisfying polynomial identities, rings of quotients, group rings, homological algebra, injectivity and itsgeneralizations, etc. Included are also applications of r ing theory to problems in coding theory and in linear algebra
Note:Springer eBooks
Contents:Foreward
Biographical sketch of S.K. Jain
Applications of Cogalois theory to elementary field arithmetic
On big lattices of classes of R
modules defined by closure properties
Reversible and duo group rings
Principally quasi
Baer ring hulls
Strongly prime ideals of near
rings of continuous functions
Elements of minimal prime ideals in general rings
The Camps
Dicks theorem
Applications of the stone duality in the theory of precompact Boolean rings
Over rings and functors
On some classes of repeated
root constacyclic codes of length a power of 2 over Galois Rings
ISBN:9783034602860
Series:e-books
Series:SpringerLink (Online service)
Series:Trends in Mathematics
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra
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Call number:SPRINGER-2010-9781849965040:ONLINE Show nearby items on shelf
Title:Group Identities on Units and Symmetric Units of Group Rings [electronic resource]
Author(s): Gregory T Lee
Date:2010
Publisher:London : Springer London
Size:1 online resource
Note:Springer e-book platform
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Note:Let FG be the group ring of a group G over a field F. Write U(FG) for the group of units of FG. It is an important problem to determine the conditions under which U(FG) satisfies a group identity. In the mid 1990s, a conjectureof Hartley was verified , namely, if U(FG) satisfies a group identity, and G is torsion, then FG satisfies a polynomial identity. Necessary and sufficient conditions for U(FG) to satisfy a group identity soon followed. Since the late1990s, many papers have been devoted to the st udy of the symmetric units that is, those units u satisfying u* = u, where * is the involution on FG defined by sending each element of G to its inverse. The conditions under which thesesymmetric units satisfy a group identity have now been determined. Th is book presents these results for arbitrary group identities, as well as the conditions under which the unit group or the set of symmetric units satisfies severalparticular group identities of interest
Note:Springer eBooks
Contents:Group Identities on Units of Group Rings
Group Identities on Symmetric Units
Lie Identities on Symmetric Elements
Nilpotence of and
ISBN:9781849965040
Series:e-books
Series:SpringerLink (Online service)
Series:Algebra and Applications : v12
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Group theory
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Call number:SPRINGER-2010-9781441917218:ONLINE Show nearby items on shelf
Title:Lattice-ordered Rings and Modules [electronic resource]
Author(s): Stuart A Steinberg
Date:2010
Edition:First
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
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Note:This book provides an exposition of the algebraic aspects of the theory of lattice-ordered rings and lattice-ordered modules. All of the background material on rings, modules, and lattice-ordered groups necessary to make the workself-contained and ac cessible to a variety of readers is included. Steinberg includes in his presentation of the material 800+ extensive exercises of varying levels of difficulty at the end of each of the sections. The first twochapters of the book provide a thorough introduc tion to the material, while the following four chapters delve into more specific topics. Key topics include: *lattice-ordered groups, rings, and fields *archimedean $l$-groups *f-ringsand larger varieties of $l$-rings *the category of f-modules *various c ommutativity results. Filling a gap in the literature, Lattice-Ordered Rings and Modules may be used as a textbook or for self-study by graduate students andresearchers studying lattice-ordered rings and lattice-ordered modules
Note:Springer eBooks
Contents:Partially Ordered Sets and Lattices
Lattice
ordered Groups
Lattice
ordered Rings
The Category of
Modules
Lattice
ordered Fields
Additional Topics
ISBN:9781441917218
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra
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Call number:SPRINGER-2010-9780817648756:ONLINE Show nearby items on shelf
Title:Symmetry and Spaces [electronic resource] : In Honor of Gerry Schwarz
Author(s): H. E. A Campbell
Aloysius G Helminck
Hanspeter Kraft
David Wehlau
Date:2010
Publisher:Boston : Birkhuser Boston
Size:1 online resource
Note:Springer e-book platform
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Note:A group of Gerry Schwarzs colleagues and collaborators gathered at the Fields Institute in Toronto for a mathematical festschrift in honor of his 60th birthday. This volume is an outgrowth of that event, covering the widerange of mathematics to which Gerry Schwarz has either made fundamental contributions or stimulated others to pursue. The articles are a sampling of modern day algebraic geometry with associated group actions from its leading experts,with a particular focus on characteristic 0 and mo dular invariant theory. Contributors: M. Brion A. Broer D. Daigle J. Elmer P. Fleischmann G. Freudenberg D. Greb P. Heinzner A. Helminck B. Kostant H. Kraft R. J. Shank W. Traves N. R.Wallach D. Wehlau
Note:Springer eBooks
Contents:Some Basic Results on Actions of Nonaffine Algebraic Groups
On ChevalleyShephardTodds Theorem in Positive Characteristic
Families of Affine Fibrations
On the Depth of Modular Invariant Rings for the Groups
Khlerian Reduction in Steps
On Orbit Decompositions for Symmetric
Varieties
Root Systems for Levi Factors and Borelde Siebenthal Theory
Polarizations and Nullcone of Representations of Reductive Groups
Decomposing Symmetric Powers of Certain Modular Representations of Cyclic Groups
Differential Operators on Grassmann Varieties
ISBN:9780817648756
Series:e-books
Series:SpringerLink (Online service)
Series:Progress in Mathematics : v278
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Algebra , Field theory (Physics)
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Call number:SPRINGER-2010-9780817647179:ONLINE Show nearby items on shelf
Title:Introduction to Quantum Groups [electronic resource]
Author(s): George Lusztig
Date:2010
Publisher:Boston : Birkhuser Boston
Size:1 online resource
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Note:The quantum groups discussed in this book are the quantized enveloping algebras introduced by Drinfeld and Jimbo in 1985, or variations thereof. It is shown that these algebras have natural integral forms that can be specializedat roots of 1 and yiel d new objects, which include quantum versions of the semi-simple groups over fields of positive characteristic. The theory of quantum groups has led to a new, extremely rigid structure, in which the objects of thetheory are provided with canonical bases h aving rather remarkable properties. This book contains an extensive treatment of the theory of canonical bases in the framework of perverse sheaves. The theory developed in the book includesthe case of quantum affine enveloping algebras and, more generall y, the quantum analogs of the KacMoody Lie algebras. Introduction to Quantum Groups will be of interest to mathematicians working in the representation theory of Liegroups and Lie algebras, knot theorists, theoretical physicists, and graduate students. Si nce large parts of the book are independent of the theory of perverse sheaves, the work may also be used as a textbook.**************************************** There is no doubt that this volume is a very remarkable piece of work...Its appearance represen ts a landmark in the mathematical literature. Bulletin of the London Mathematical Society Thisbook is an important contribution to the field and can be recommended especially to mathematicians working in the field. EMS Newsletter The present book gives a very efficient presentation of an important part of quantum grouptheory. It is a valuable contribution to the literature. Mededelingen van het Wiskundig Lusztig's book is very well written and seems to be flawless...Obviously, this will be the standard re ference book for the material presentedand anyone interested in the DrinfeldJimbo algebras will have to study it very carefully. ZAA [T]his book is much more than an 'introduction to q
Note:Springer eBooks
Contents:Preface
Part I: The Drinfeld
Jimbo Algebra U
Part II: Geometric Realization of f
Part III: Kashiwaras Operators and Applications
Part IV: Canonical Basis of U
Part V: Change of Rings
Part VI: Braid Group Action
Index of Notation
Index of Terminology
ISBN:9780817647179
Series:e-books
Series:SpringerLink (Online service)
Series:Modern Birkhuser Classics
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Group theory , Topological Groups , Quantum theory , Mathematical physics
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Call number:SPRINGER-2009-9783764388584:ONLINE Show nearby items on shelf
Title:Selected Works of A.I. Shirshov [electronic resource]
Author(s): Leonid Bokut
Ivan Shestakov
Victor Latyshev
Efim Zelmanov
Date:2009
Publisher:Basel : Birkhuser Basel
Size:1 online resource
Note:Springer e-book platform
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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
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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-2009-9780817647278:ONLINE Show nearby items on shelf
Title:The Center and Cyclicity Problems [electronic resource] A Computational Algebra Approach
Author(s): Douglas Shafer
Valery Romanovski
Date:2009
Publisher:Boston : Birkhuser Boston
Size:1 online resource
Note:Springer e-book platform
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Note:In the last three decades, advances in methods for investigating polynomial ideals and their varieties have provided new possibilities for approaching two long-standing problems in the theory of differential equations: thePoincar center problem and t he cyclicity problem (the problem of bifurcation of limit cycles from singular trajectories). Using a computational algebra approach, this work addresses the center and cyclicity problems as behaviors ofdynamical systems and families of polynomial systems . The text first lays the groundwork for computational algebra and gives the main properties of ideals in polynomial rings and their affine varieties this is followed by a discussionregarding the theory of normal forms and stability of differential equati ons. The center and cyclicity problems are then explored in detail. The book contains numerous examples, pseudocode displays of all the computational algorithms,historical notes, nearly two hundred exercises, and an extensive bibliography. Completely self -contained, it is thus suitable mainly as a textbook for a graduate course in the subject but also as a reference for researchers
Note:Springer eBooks
Contents:Polynomial Ideals and Their Varieties
Stability and Normal Forms
The Center Problem
The Isochronicity and Linearizability Problems
Invariants of the Rotation Group
Bifurcations of Limit Cycles and Critical Periods
ISBN:9780817647278
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Field theory (Physics) , Differentiable dynamical systems , Differential Equations , Differential equations, partial , Computer science Mathematics
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Call number:SPRINGER-2009-9780387787534:ONLINE Show nearby items on shelf
Title:Introduction to Siegel Modular Forms and Dirichlet Series [electronic resource]
Author(s): Anatoli Andrianov
Date:2009
Publisher:New York, NY : Springer US
Size:1 online resource
Note:Springer e-book platform
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Note:Introduction to Siegel Modular Forms and Dirichlet Series gives a concise and self-contained introduction to the multiplicative theory of Siegel modular forms, Hecke operators, and zeta functions, including the classical case ofmodular forms in one v ariable. It serves to attract young researchers to this beautiful field and makes the initial steps more pleasant. It treats a number of questions that are rarely mentioned in other books. It is the first and onlybook so far on Siegel modular forms that i ntroduces such important topics as analytic continuation and the functional equation of spinor zeta functions of Siegel modular forms of genus two. Unique features include: * New, simplifiedapproaches and a fresh outlook on classical problems * The abstra ct theory of HeckeShimura rings for symplectic and related groups * The action of Hecke operators on Siegel modular forms * Applications of Hecke operators to astudy of the multiplicative properties of Fourier coefficients of modular forms * The proof of analytic continuation and the functional equation (under certain assumptions) for Euler products associated with modular forms of genus two*Numerous exercises Anatoli Andrianov is a leading researcher at the St. Petersburg branch of the Steklov Mathematic al Institute of the Russian Academy of Sciences. He is well known for his works on the arithmetic theory of automorphicfunctions and quadratic forms, a topic on which he has lectured at many universities around the world
Note:Springer eBooks
Contents:Preface
Introduction: The Two Features of Arithmetical Zeta Functions
Modular Forms
Dirichlet Series of Modular Forms
Hecke
Shimura Rings of Double Cosets
Hecke Operators
Euler Factorization of Radial Series
Conclusion: Other Groups, Other Horizons
Notes
Short Bibliography
ISBN:9780387787534
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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