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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 |
Availability: | Click
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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 |
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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 |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
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 |
Note: | Springer e-book platform |
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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 |
Note: | Springer e-book platform |
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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 |
Note: | Springer 2013 e-book collections |
Note: | At first sight, finitely generated abelian groups and canonical forms of matrices appear to have little in common. However, reduction to Smith normal form, named after its originator H.J.S.Smith in 1861, is a matrix version ofthe Euclidean algorithm and is exactly what the theory requires in both cases. Starting with matrices over the integers, Part1 of this book provides a measured introduction to such groups: two finitely generated abelian groups areisomorphic if and only if their invariant factor sequences are identical. The analogous theory of matrix similarity over a field is then developed in Part2 starting with matrices having polynomial entries: two matrices over a fieldare similar if and only if their rational canonical forms are equal. Unde r certain conditions each matrix is similar to a diagonal or nearly diagonal matrix, namely its Jordan form. The reader is assumed to be familiar with theelementary properties of rings and fields. Also a knowledge of abstract linear algebra including vect or spaces, linear mappings, matrices, bases and dimension is essential, although much of the theory is covered in the text but froma more general standpoint: the role of vector spaces is widened to modules over commutative rings. Based on a lecture course taught by the author for nearly thirty years, the book emphasises algorithmic techniques and features numerousworked examples and exercises with solutions. The early chapters form an ideal second course in algebra for second and third year undergraduates . The later chapters, which cover closely related topics, e.g. field extensions,endomorphism rings, automorphism groups, and variants of the canonical forms, will appeal to more advanced students. The book is a bridge between linear and abstract algebra |
Note: | Springer eBooks |
Contents: | Part 1 :Finitely Generated Abelian Groups: Matrices with Integer Entries: The Smith Normal Form |
Basic Theory of Additive Abelian Groups | |
Decomposition of Finitely Generated Z | |
Modules. Part 2: Similarity of Square Matrices over a Field: The Polynomial Ring F[x]and Matrices over F[x] | |
F[x] Modules: Similarity of t xtMatrices over a Field F | |
Canonical Forms and Similarity Classes of Square Matrices over a Field. | |
ISBN: | 9781447127307 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Undergraduate Mathematics Series, 1615-2085 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Field theory (Physics) , Group theory , Matrix theory , Algorithms |
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Call number: | SPRINGER-2012-9781447122944: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 |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Sheaves of Algebras over Boolean Spaces comprehensively covers sheaf theory as applied to universal algebra. Sheaves decompose general algebras into simpler pieces called the stalks. A classical case is commutative von Neumannregular rings, whose sta lks are fields. Other classical theorems also extend to shells, a common generalization of rings and lattices. This text presents intuitive ideas from topology such as the notion of metric space and the conceptof central idempotent from ring theory. These lead to the abstract notions of complex and factor element, respectively. Factor elements are defined by identities, discovered for shells for the first time, explaining why centralelements in rings and lattices have their particular form. Categorical fo rmulations of the many representations by sheaves begin with adjunctions and move to equivalences as the book progresses, generalizing Stones theorem forBoolean algebras. Half of the theorems provided in the text are new the rest are presented in a cohere nt framework, starting with the most general, and proceeding to specific applications. Many open problems and research areas areoutlined, including a final chapter summarizing applications of sheaves in diverse fields that were not covered earlier in the book. This monograph is suitable for graduate students and researchers, and it will serve as an excellentreference text for those who wish to learn about sheaves of algebras |
Note: | Springer eBooks |
Contents: | Preface |
Introduction | |
Algebra | |
Tools | |
Complexes and their Sheaves | |
Boolean Subsemilattices | |
Sheaves from Factor Congruences | |
Shells | |
Baer | |
Stone Shells | |
Strict Shells | |
Varieties Generated by Preprimal Algebras | |
Return to General Algebras | |
Further Examples Pointing to Future Research | |
List of Symbols | |
References | |
Index | |
ISBN: | 9780817646424 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Topology |
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Call number: | SPRINGER-2011-9783642217746: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 |
Note: | Springer 2013 e-book collections |
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 |
Note: | Springer 2013 e-book collections |
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 |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book covers the modular invariant theory of finite groups, the case when the characteristic of the field divides the order of the group. It explains a theory that is more complicated than the study of the classicalnon-modular case, and it descri bes many open questions. Largely self-contained, the book develops the theory from its origins up to modern results. It explores many examples, illustrating the theory and its contrast with the betterunderstood non-modular setting. It details techniques f or the computation of invariants for many modular representations of finite groups, especially the case of the cyclic group of prime order. It includes detailed examples of manytopics as well as a quick survey of the elements of algebraic geometry and com mutative algebra as they apply to invariant theory. The book is aimed at both graduate students and researchersan introduction to many important topics inmodern algebra within a concrete setting for the former, an exploration of a fascinating subfield of algebraic geometry for the latter |
Note: | Springer eBooks |
Contents: | 1 First Steps |
2 Elements of Algebraic Geometry and Commutative Algebra | |
3 Applications of Commutative Algebra to Invariant Theory | |
4 Examples | |
5 Monomial Orderings and SAGBI Bases | |
6 Block Bases | |
7 The Cyclic Group Cp | |
8 Polynomial Invariant Rings | |
9 The Transfer | |
10 Invariant Rings via Localization | |
11 Rings of Invariants which are Hypersurfaces | |
12 Separating Invariants | |
13 Using SAGBI Bases to Compute Rings of Invariants | |
14 Ladders | |
References | |
Index | |
ISBN: | 9783642174049 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Encyclopaedia of Mathematical Sciences, 0938-0396 : v139 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Geometry, algebraic |
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Call number: | SPRINGER-2011-9783642151286: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 |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This textbook offers a thorough, modern introduction into commutative algebra. It is intented mainly to serve as a guide for a course of one or two semesters, or for self-study. The carefully selected subject matter concentrateson the concepts and re sults at the center of the field. The book maintains a constant view on the natural geometric context, enabling the reader to gain a deeper understanding of the material. Although it emphasizes theory, threechapters are devoted to computational aspects. M any illustrative examples and exercises enrich the text |
Note: | Springer eBooks |
Contents: | Introduction |
Part I The Algebra Geometry Lexicon: 1 Hilbert's Nullstellensatz 2 Noetherian and Artinian Rings 3 The Zariski Topology 4 A Summary of the Lexicon | |
Part II Dimension: 5 Krull Dimension and Transcendence Degree 6 Localization 7 The Principal Ideal Theorem 8 Integral Extensions | |
Part III Computational Methods: 9 Grbner Bases 10 Fibers and Images of Morphisms Revisited 11 Hilbert Series and Dimension | |
Part IV Local Rings: 12 Dimension Theory 13 Regular Local Rings 14 Rings of Dimension One | |
References | |
Notation | |
Index | |
ISBN: | 9783642035456 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Graduate Texts in Mathematics, 0072-5285 : v256 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Algebra , Computer science Mathematics |
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Call number: | SPRINGER-2011-9781441969903:ONLINE Show nearby items on shelf |
Title: | Commutative Algebra [electronic resource] : Noetherian and Non-Noetherian Perspectives |
Author(s): |
Marco Fontana Salah-Eddine Kabbaj Bruce Olberding Irena Swanson |
Date: | 2011 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Commutative algebra is a rapidly growing subject that is developing in many different directions. This volume presents several of the most recent results from various areas related to both Noetherian and non-Noetherian commutativealgebra. This volume contains a collection of invited survey articles by some of the leading experts in the field. The authors of these chapters are internationally renowned for their important contributions to various aspects ofcurrent research in commutative algebra. Some topics presented in the volume include: generalizations of cyclic modules, zero divisor graphs, class semigroups, forcing algebras, syzygy bundles, tight closure, Gorenstein dimensions,tensor products of algebras over fields, as well as many others. This book is intended for researchers and graduate students interested in studying commutative algebra |
Note: | Springer eBooks |
Contents: | Introduction |
1. Principal | |
like Ideals and Related Polynomial Content Conditions (D.D. Anderson) | |
2. Zero | |
divisor Graphs in Commutative Rings (D.F. Anderson, M. Axtell, J. Stickles) | |
3. Class Semigroups and T | |
class Semigroups of Domains (S. Bazzoni, S. Kabbaj) | |
4. Forcing Algebras, Syzygy Bundles, and Tight Closure (H. Brenner) | |
5. Beyond Totally Reflexive Modules and Back: A Survey on Gorenstein Dimensions (L.W. Christensen, H.B. Foxby, H. Holm) | |
6. On V | |
domains: A Survey (M. Fontana, M. Zafrullah) | |
7. Tensor Products of Algebras Over a Field (H. Haghighi, M. Tousi, S. Yassemi | |
ISBN: | 9781441969903 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Algebra |
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Call number: | SPRINGER-2011-9780857298508: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 |
Note: | Springer 2013 e-book collections |
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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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 |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
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 |
Note: | Springer e-book platform |
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 |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
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 |
Note: | Springer 2013 e-book collections |
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 |
Note: | Springer 2013 e-book collections |
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 |
Availability: | Click here to see Library holdings or inquire at
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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 |
Note: | Springer 2013 e-book collections |
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 |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
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 |
Note: | Springer 2013 e-book collections |
Note: | This book presents translations of selected works of the famous Russian mathematician A.I. Shirshov (19211981). He was a pioneer in several directions of associative, Lie, Jordan, and alternative algebras, as well as groupsand projective planes. His name is associated with notions and results on Grbner-Shirshov bases, the Composition-Diamond Lemma, the Shirshov-Witt Theorem, the Lazard-Shirshov elimination process, Shirshovs Height Theorem,Lyndon-Shirshov words, Hall-Shirshov bases, Shirshovs theorem on the Kurosh problem for alternative and Jordan algebras, and Shirshovs theorem on the speciality of Jordan algebras with two generators. Shirshovs ideas were usedby his student Efim Zelmanov for the solution of the Restricted Burnside Problem. Several famous algebraists provide in this book detailed comments on the impact of Shirshovs work on current algebra |
Note: | Springer eBooks |
Contents: | From the contents: Publications of A.I. Shirshov: Subalgebras of free Lie algebras |
On the representation of Lie rings in associative rings | |
Subalgebras of free commutative and free anticommutative algebras | |
On special J | |
rings | |
Some theorems on embedding of rings | |
On some nonassociative nil | |
rings and algebraic algebras | |
On rings with identical relations | |
On free Lie rings | |
On a problem of Levitzki | |
Some problems in the theory of rings that are nearly associative | |
Some algorithmic problems for e | |
algebras | |
Some algorithmic problems for Lie algebras | |
On a hypothesis in the | |
ISBN: | 9783764388584 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Contemporary Mathematicians |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Mathematics_$xHistory |
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Call number: | SPRINGER-2009-9781848829411:ONLINE Show nearby items on shelf |
Title: | Group and Ring Theoretic Properties of Polycyclic Groups [electronic resource] |
Author(s): |
B.A.F Wehrfritz |
Date: | 2009 |
Publisher: | London : Springer London |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Polycyclic groups are built from cyclic groups in a specific way. They arise in many contexts within group theory itself but also more generally in algebra, for example in the theory of Noetherian rings. They also touch on someaspects of topology, ge ometry and number theory. The first half of this book develops the standard group theoretic techniques for studying polycyclic groups and the basic properties of these groups. The second half then focusesspecifically on the ring theoretic properties of po lycyclic groups and their applications, often to purely group theoretic situations. The book is not intended to be encyclopedic. Instead, it is a study manual for graduate students andresearchers coming into contact with polycyclic groups, where the main lines of the subject can be learned from scratch by any reader who has been exposed to some undergraduate algebra, especially groups, rings and vector spaces. Thusthe book has been kept short and readable with a view that it can be read and worked through from cover to cover. At the end of each topic covered there is a description without proofs, but with full references, of further developmentsin the area. The book then concludes with an extensive bibliography of items relating to polycyclic groups |
Note: | Springer eBooks |
Contents: | Foreword |
Some basic group theory | |
Some ring theory | |
Soluble linear groups | |
Further group | |
theoretic properties of polycyclic groups | |
Groups acting on finitely generated commutative rings | |
Prime ideals in polycyclic | |
group rings | |
The structure of modules over polycyclic groups | |
Semilinear and skew linear groups | |
ISBN: | 9781848829411 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Algebra and Applications : v10 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Group theory |
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Call number: | SPRINGER-2009-9780817647278: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 |
Note: | Springer 2013 e-book collections |
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 |
Note: | Springer 2013 e-book collections |
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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