Algebras Rings And Their Representations

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Algebras, Rings And Their Representations - Proceedings Of The International Conference On Algebras, Modules And Rings

Alberto Facchini,Kent Fuller,Claus M Ringel,Catarina Santa-clara
Algebras Rings And Their Representations Proceedings Of The International Conference On Algebras Modules And Rings Book PDF

Author : Alberto Facchini,Kent Fuller,Claus M Ringel,Catarina Santa-clara
Publisher : World Scientific
Page : 403 pages
File Size : 49,9 Mb
Release : 2006-02-20
Category : Mathematics
ISBN : 9789814478977

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Algebras, Rings And Their Representations - Proceedings Of The International Conference On Algebras, Modules And Rings by Alberto Facchini,Kent Fuller,Claus M Ringel,Catarina Santa-clara Pdf

Surveying the most influential developments in the field, this proceedings reviews the latest research on algebras and their representations, commutative and non-commutative rings, modules, conformal algebras, and torsion theories.The volume collects stimulating discussions from world-renowned names including Tsit-Yuen Lam, Larry Levy, Barbara Osofsky, and Patrick Smith.

Algebras, Rings and Their Representations

Alberto Facchini
Algebras Rings and Their Representations Book PDF

Author : Alberto Facchini
Publisher : World Scientific
Page : 403 pages
File Size : 49,6 Mb
Release : 2006
Category : Mathematics
ISBN : 9789812774552

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Algebras, Rings and Their Representations by Alberto Facchini Pdf

Surveying the most influential developments in the field, this proceedings reviews the latest research on algebras and their representations, commutative and non-commutative rings, modules, conformal algebras, and torsion theories. The volume collects stimulating discussions from world-renowned names including Tsit-Yuen Lam, Larry Levy, Barbara Osofsky, and Patrick Smith. Sample Chapter(s). Chapter 1: Some Coreflective Categories of Topological Modules (221 KB). Contents: Krull Monoids and Their Application in Module Theory (A Facchini); Infinite Progenerator Sums (A Facchini & L S Levy); Quadratic Algebras of Skew Type (E Jespers & J Okn nski); Representation Type of Commutative Noetherian Rings (Introduction) (L Klingler & L S Levy); Corner Ring Theory: A Generalization of Peirce Decompositions (T-Y Lam); Quasideterminants and Right Roots of Polynomials Over Division Rings (B L Osofsky); Injective Dimension Relative to a Torsion Theory (P F Smith); and other papers. Readership: Algebraists, mathematicians interested in the connections between algebra and other fields, and graduate students interested in algebra."

Introduction to Vertex Operator Algebras and Their Representations

James Lepowsky,Haisheng Li
Introduction to Vertex Operator Algebras and Their Representations Book PDF

Author : James Lepowsky,Haisheng Li
Publisher : Springer Science & Business Media
Page : 330 pages
File Size : 46,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9780817681869

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Introduction to Vertex Operator Algebras and Their Representations by James Lepowsky,Haisheng Li Pdf

* Introduces the fundamental theory of vertex operator algebras and its basic techniques and examples. * Begins with a detailed presentation of the theoretical foundations and proceeds to a range of applications. * Includes a number of new, original results and brings fresh perspective to important works of many other researchers in algebra, lie theory, representation theory, string theory, quantum field theory, and other areas of math and physics.

Rings with Polynomial Identities and Finite Dimensional Representations of Algebras

Eli Aljadeff,Antonio Giambruno,Claudio Procesi,Amitai Regev
Rings with Polynomial Identities and Finite Dimensional Representations of Algebras Book PDF

Author : Eli Aljadeff,Antonio Giambruno,Claudio Procesi,Amitai Regev
Publisher : American Mathematical Soc.
Page : 630 pages
File Size : 50,6 Mb
Release : 2020-12-14
Category : Education
ISBN : 9781470451745

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Rings with Polynomial Identities and Finite Dimensional Representations of Algebras by Eli Aljadeff,Antonio Giambruno,Claudio Procesi,Amitai Regev Pdf

A polynomial identity for an algebra (or a ring) A A is a polynomial in noncommutative variables that vanishes under any evaluation in A A. An algebra satisfying a nontrivial polynomial identity is called a PI algebra, and this is the main object of study in this book, which can be used by graduate students and researchers alike. The book is divided into four parts. Part 1 contains foundational material on representation theory and noncommutative algebra. In addition to setting the stage for the rest of the book, this part can be used for an introductory course in noncommutative algebra. An expert reader may use Part 1 as reference and start with the main topics in the remaining parts. Part 2 discusses the combinatorial aspects of the theory, the growth theorem, and Shirshov's bases. Here methods of representation theory of the symmetric group play a major role. Part 3 contains the main body of structure theorems for PI algebras, theorems of Kaplansky and Posner, the theory of central polynomials, M. Artin's theorem on Azumaya algebras, and the geometric part on the variety of semisimple representations, including the foundations of the theory of Cayley–Hamilton algebras. Part 4 is devoted first to the proof of the theorem of Razmyslov, Kemer, and Braun on the nilpotency of the nil radical for finitely generated PI algebras over Noetherian rings, then to the theory of Kemer and the Specht problem. Finally, the authors discuss PI exponent and codimension growth. This part uses some nontrivial analytic tools coming from probability theory. The appendix presents the counterexamples of Golod and Shafarevich to the Burnside problem.

Algebras, Rings and Modules

Michiel Hazewinkel,Nadiya Gubareni,V.V. Kirichenko
Algebras Rings and Modules Book PDF

Author : Michiel Hazewinkel,Nadiya Gubareni,V.V. Kirichenko
Publisher : Springer Science & Business Media
Page : 405 pages
File Size : 43,6 Mb
Release : 2007-09-08
Category : Mathematics
ISBN : 9781402051418

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Algebras, Rings and Modules by Michiel Hazewinkel,Nadiya Gubareni,V.V. Kirichenko Pdf

This second volume of this text covers the classical aspects of the theory of groups and their representations. It also offers a general introduction to the modern theory of representations including the representations of quivers and finite partially ordered sets and their applications to finite dimensional algebras. It reviews key recent developments in the theory of special ring classes including Frobenius, quasi-Frobenius, and others.

Three Papers on Algebras and Their Representations

V. N. Gerasimov,N. G. Nesterenko,A. I. Valitskas
Three Papers on Algebras and Their Representations Book PDF

Author : V. N. Gerasimov,N. G. Nesterenko,A. I. Valitskas
Publisher : American Mathematical Soc.
Page : 226 pages
File Size : 50,5 Mb
Release : 1993
Category : Mathematics
ISBN : 0821875035

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Three Papers on Algebras and Their Representations by V. N. Gerasimov,N. G. Nesterenko,A. I. Valitskas Pdf

This book contains the doctoral dissertations of three students from Novosibirsk who participated in the seminar of L. A. Bokut'. The dissertation of Gerasimov focuses on Cohn's theory of noncommutative matrix localizations. Gerasimov presents a construction of matrix localization that is not directly related to (prime) matrix ideals of Cohn, but rather deals with localizations of arbitrary subsets of matrices over a ring. The work of Valitskas applies ideas and constructions of Gerasimov to embeddings of rings into radical rings (in the sense of Jacobson) to develop a theory essentially parallel to Cohn's theory of embeddings of rings into skew fields. Nesterenko's dissertation solves some important problems of Anan'in and Bergman about representations of (infinite-dimensional) algebras and categories in (triangular) matrices over commutative rings.

Algebras and Representation Theory

Karin Erdmann,Thorsten Holm
Algebras and Representation Theory Book PDF

Author : Karin Erdmann,Thorsten Holm
Publisher : Springer
Page : 304 pages
File Size : 44,6 Mb
Release : 2018-09-07
Category : Mathematics
ISBN : 9783319919980

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Algebras and Representation Theory by Karin Erdmann,Thorsten Holm Pdf

This carefully written textbook provides an accessible introduction to the representation theory of algebras, including representations of quivers. The book starts with basic topics on algebras and modules, covering fundamental results such as the Jordan-Hölder theorem on composition series, the Artin-Wedderburn theorem on the structure of semisimple algebras and the Krull-Schmidt theorem on indecomposable modules. The authors then go on to study representations of quivers in detail, leading to a complete proof of Gabriel's celebrated theorem characterizing the representation type of quivers in terms of Dynkin diagrams. Requiring only introductory courses on linear algebra and groups, rings and fields, this textbook is aimed at undergraduate students. With numerous examples illustrating abstract concepts, and including more than 200 exercises (with solutions to about a third of them), the book provides an example-driven introduction suitable for self-study and use alongside lecture courses.

Algebras, Rings, and Modules

Michiel Hazewinkel,Nadezhda Mikhaĭlovna Gubareni
Algebras Rings and Modules Book PDF

Author : Michiel Hazewinkel,Nadezhda Mikhaĭlovna Gubareni
Publisher : CRC Press
Page : 0 pages
File Size : 54,5 Mb
Release : 2016
Category : Modules (Algebra).
ISBN : 1138035823

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Algebras, Rings, and Modules by Michiel Hazewinkel,Nadezhda Mikhaĭlovna Gubareni Pdf

Volume 3," ... systematizes and presents the main results of the structure theory of some special classes of non-commutative rings. The book presents both the basic classical theory and more recent results related to current research such as the structure theory of some special classes of rings, which arise in many applications. Some of the topics covered include quivers, partially ordered sets and their representations, as well as such special rings as hereditary and semihereditary rings, serial rings, semidistrubutive rings and modules over them" (from preface).

Identities of Algebras and their Representations

I︠U︡riĭ Pitrimovich Razmyslov
Identities of Algebras and their Representations Book PDF

Author : I︠U︡riĭ Pitrimovich Razmyslov
Publisher : American Mathematical Soc.
Page : 468 pages
File Size : 54,8 Mb
Release : 1994
Category : Mathematics
ISBN : 0821846086

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Identities of Algebras and their Representations by I︠U︡riĭ Pitrimovich Razmyslov Pdf

During the past forty years, a new trend in the theory of associative algebras, Lie algebras, and their representations has formed under the influence of mathematical logic and universal algebra, namely, the theory of varieties and identities of associative algebras, Lie algebras, and their representations. The last twenty years have seen the creation of the method of 2-words and *a-functions, which allowed a number of problems in the theory of groups, rings, Lie algebras, and their representations to be solved in a unified way. The possibilities of this method are far from exhausted. This book sums up the applications of the method of 2-words and *a-functions in the theory of varieties and gives a systematic exposition of contemporary achievements in the theory of identities of algebras and their representations closely related to this method. The aim is to make these topics accessible to a wider group of mathematicians.

Algebras, Rings and Modules

Michiel Hazewinkel,Nadiya M. Gubareni
Algebras Rings and Modules Book PDF

Author : Michiel Hazewinkel,Nadiya M. Gubareni
Publisher : CRC Press
Page : 388 pages
File Size : 45,9 Mb
Release : 2016-04-05
Category : Mathematics
ISBN : 9781482245059

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Algebras, Rings and Modules by Michiel Hazewinkel,Nadiya M. Gubareni Pdf

The theory of algebras, rings, and modules is one of the fundamental domains of modern mathematics. General algebra, more specifically non-commutative algebra, is poised for major advances in the twenty-first century (together with and in interaction with combinatorics), just as topology, analysis, and probability experienced in the twentieth century. This volume is a continuation and an in-depth study, stressing the non-commutative nature of the first two volumes of Algebras, Rings and Modules by M. Hazewinkel, N. Gubareni, and V. V. Kirichenko. It is largely independent of the other volumes. The relevant constructions and results from earlier volumes have been presented in this volume.

Rings, Modules and Representations

Viet Dung Nguyen
Rings Modules and Representations Book PDF

Author : Viet Dung Nguyen
Publisher : American Mathematical Soc.
Page : 377 pages
File Size : 52,7 Mb
Release : 2009
Category : Mathematics
ISBN : 9780821843703

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Rings, Modules and Representations by Viet Dung Nguyen Pdf

The papers in this volume contain results in active research areas in the theory of rings and modules, including non commutative and commutative ring theory, module theory, representation theory, and coding theory.

Algebras, Rings and Modules, Volume 2

Michiel Hazewinkel,Nadiya M. Gubareni
Algebras Rings and Modules Volume 2 Book PDF

Author : Michiel Hazewinkel,Nadiya M. Gubareni
Publisher : CRC Press
Page : 364 pages
File Size : 46,5 Mb
Release : 2017-04-11
Category : Mathematics
ISBN : 9781351869874

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Algebras, Rings and Modules, Volume 2 by Michiel Hazewinkel,Nadiya M. Gubareni Pdf

The theory of algebras, rings, and modules is one of the fundamental domains of modern mathematics. General algebra, more specifically non-commutative algebra, is poised for major advances in the twenty-first century (together with and in interaction with combinatorics), just as topology, analysis, and probability experienced in the twentieth century. This is the second volume of Algebras, Rings and Modules: Non-commutative Algebras and Rings by M. Hazewinkel and N. Gubarenis, a continuation stressing the more important recent results on advanced topics of the structural theory of associative algebras, rings and modules.

Algebras, Rings and Modules

Michiel Hazewinkel,Nadiya Gubareni,V.V. Kirichenko
Algebras Rings and Modules Book PDF

Author : Michiel Hazewinkel,Nadiya Gubareni,V.V. Kirichenko
Publisher : Springer
Page : 400 pages
File Size : 51,7 Mb
Release : 2009-09-03
Category : Mathematics
ISBN : 9048110025

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Algebras, Rings and Modules by Michiel Hazewinkel,Nadiya Gubareni,V.V. Kirichenko Pdf

This second volume of this text covers the classical aspects of the theory of groups and their representations. It also offers a general introduction to the modern theory of representations including the representations of quivers and finite partially ordered sets and their applications to finite dimensional algebras. It reviews key recent developments in the theory of special ring classes including Frobenius, quasi-Frobenius, and others.

Lie Algebras and Their Representations

Seok-Jin Kang,Myung-Hwan Kim,Insok Lee
Lie Algebras and Their Representations Book PDF

Author : Seok-Jin Kang,Myung-Hwan Kim,Insok Lee
Publisher : American Mathematical Soc.
Page : 242 pages
File Size : 40,9 Mb
Release : 1996
Category : Mathematics
ISBN : 9780821805121

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Lie Algebras and Their Representations by Seok-Jin Kang,Myung-Hwan Kim,Insok Lee Pdf

Over the past 30 years, exciting developments in diverse areas of the theory of Lie algebras and their representations have been observed. The symposium covered topics such as Lie algebras and combinatorics, crystal bases for quantum groups, quantum groups and solvable lattice models, and modular and infinite-dimensional Lie algebras. In this volume, readers will find several excellent expository articles and research papers containing many significant new results in this area.

Representations of Algebras and Related Topics

Andrzej Skowroński,Kunio Yamagata
Representations of Algebras and Related Topics Book PDF

Author : Andrzej Skowroński,Kunio Yamagata
Publisher : European Mathematical Society
Page : 744 pages
File Size : 42,9 Mb
Release : 2011
Category : Algebra
ISBN : 3037191015

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Representations of Algebras and Related Topics by Andrzej Skowroński,Kunio Yamagata Pdf

This book, which explores recent trends in the representation theory of algebras and its exciting interaction with geometry, topology, commutative algebra, Lie algebras, combinatorics, quantum algebras, and theoretical field, is conceived as a handbook to provide easy access to the present state of knowledge and stimulate further development. The many topics discussed include quivers, quivers with potential, bound quiver algebras, Jacobian algebras, cluster algebras and categories, Calabi-Yau algebras and categories, triangulated and derived categories, and quantum loop algebras. This book consists of thirteen self-contained expository survey and research articles and is addressed to researchers and graduate students in algebra as well as a broader mathematical community. The articles contain a large number of examples and open problems and give new perspectives for research in the field.