Noncommutative Rings And Their Applications

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Noncommutative Rings, Group Rings, Diagram Algebras and Their Applications

Surender Kumar Jain,S. Parvathi,Dinesh Khurana
Noncommutative Rings Group Rings Diagram Algebras and Their Applications Book PDF

Author : Surender Kumar Jain,S. Parvathi,Dinesh Khurana
Publisher : American Mathematical Soc.
Page : 242 pages
File Size : 55,9 Mb
Release : 2008
Category : Mathematics
ISBN : 9780821842850

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Noncommutative Rings, Group Rings, Diagram Algebras and Their Applications by Surender Kumar Jain,S. Parvathi,Dinesh Khurana Pdf

Articles in this volume are based on talks given at the International Conference on Noncommutative Rings, Group Rings, Diagram Algebras and Their Applications. The conference provided researchers in mathematics with the opportunity to discuss new developments in these rapidly growing fields. This book contains several excellent articles, both expository and original, with new and significant results. It is suitable for graduate students and researchers interested in Ring Theory,Diagram Algebras and related topics.

Noncommutative Rings and Their Applications

Steven Dougherty,Alberto Facchini,Andre Gerard Leroy,Edmund Puczylowski,Patrick Sole
Noncommutative Rings and Their Applications Book PDF

Author : Steven Dougherty,Alberto Facchini,Andre Gerard Leroy,Edmund Puczylowski,Patrick Sole
Publisher : American Mathematical Soc.
Page : 280 pages
File Size : 47,8 Mb
Release : 2015-02-20
Category : Mathematics
ISBN : 9781470410322

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Noncommutative Rings and Their Applications by Steven Dougherty,Alberto Facchini,Andre Gerard Leroy,Edmund Puczylowski,Patrick Sole Pdf

Contains the Proceedings of an International Conference on Noncommutative Rings and Their Applications, held July 1-4, 2013, at the Universite d'Artois, Lens, France. It presents recent developments in the theories of noncommutative rings and modules over such rings as well as applications of these to coding theory, enveloping algebras, and Leavitt path algebras.

Noncommutative Rings

I. N. Herstein
Noncommutative Rings Book PDF

Author : I. N. Herstein
Publisher : American Mathematical Soc.
Page : 202 pages
File Size : 54,6 Mb
Release : 1994-12-31
Category : Mathematics
ISBN : 9780883850152

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Noncommutative Rings by I. N. Herstein Pdf

Noncommutative Rings provides a cross-section of ideas, techniques, and results that give the reader an idea of that part of algebra which concerns itself with noncommutative rings. In the space of 200 pages, Herstein covers the Jacobson radical, semisimple rings, commutativity theorems, simple algebras, representations of finite groups, polynomial identities, Goldie's theorem, and the Golod–Shafarevitch theorem. Almost every practicing ring theorist has studied portions of this classic monograph.

Noncommutative Algebraic Geometry and Representations of Quantized Algebras

A. Rosenberg
Noncommutative Algebraic Geometry and Representations of Quantized Algebras Book PDF

Author : A. Rosenberg
Publisher : Springer Science & Business Media
Page : 333 pages
File Size : 42,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401584302

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Noncommutative Algebraic Geometry and Representations of Quantized Algebras by A. Rosenberg Pdf

This book is based on lectures delivered at Harvard in the Spring of 1991 and at the University of Utah during the academic year 1992-93. Formally, the book assumes only general algebraic knowledge (rings, modules, groups, Lie algebras, functors etc.). It is helpful, however, to know some basics of algebraic geometry and representation theory. Each chapter begins with its own introduction, and most sections even have a short overview. The purpose of what follows is to explain the spirit of the book and how different parts are linked together without entering into details. The point of departure is the notion of the left spectrum of an associative ring, and the first natural steps of general theory of noncommutative affine, quasi-affine, and projective schemes. This material is presented in Chapter I. Further developments originated from the requirements of several important examples I tried to understand, to begin with the first Weyl algebra and the quantum plane. The book reflects these developments as I worked them out in reallife and in my lectures. In Chapter 11, we study the left spectrum and irreducible representations of a whole lot of rings which are of interest for modern mathematical physics. The dasses of rings we consider indude as special cases: quantum plane, algebra of q-differential operators, (quantum) Heisenberg and Weyl algebras, (quantum) enveloping algebra ofthe Lie algebra sl(2) , coordinate algebra of the quantum group SL(2), the twisted SL(2) of Woronowicz, so called dispin algebra and many others.

Rings, Modules and Codes

André Leroy,Christian Lomp,Sergio López-Permouth,Frédérique Oggier
Rings Modules and Codes Book PDF

Author : André Leroy,Christian Lomp,Sergio López-Permouth,Frédérique Oggier
Publisher : American Mathematical Soc.
Page : 355 pages
File Size : 51,9 Mb
Release : 2019-04-12
Category : Modules (Algebra)
ISBN : 9781470441043

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Rings, Modules and Codes by André Leroy,Christian Lomp,Sergio López-Permouth,Frédérique Oggier Pdf

This book contains the proceedings of the Fifth International Conference on Noncommutative Rings and their Applications, held from June 12–15, 2017, at the University of Artois, Lens, France. The papers are related to noncommutative rings, covering topics such as: ring theory, with both the elementwise and more structural approaches developed; module theory with popular topics such as automorphism invariance, almost injectivity, ADS, and extending modules; and coding theory, both the theoretical aspects such as the extension theorem and the more applied ones such as Construction A or Reed–Muller codes. Classical topics like enveloping skewfields, weak Hopf algebras, and tropical algebras are also presented.

Noncommutative Rings

Susan Montgomery,Lance Small
Noncommutative Rings Book PDF

Author : Susan Montgomery,Lance Small
Publisher : Springer Science & Business Media
Page : 182 pages
File Size : 50,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461397366

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Noncommutative Rings by Susan Montgomery,Lance Small Pdf

This volume collects some of the survey lectures delivered at the Micro program on Noncommutative Rings held at MSRI, July 10-21, 1989. While the program was concerned with recent advances in ring theory, it also had as an important component lectures on related areas of mathematics where ring theory might be expected to have an impact. Thus, there are lectures of S. P. Smith on quantum groups and Marc Ri effel on algebraic aspects of quantum field theory. Martin Lorenz and Don ald Passman consider in their lectures various aspects of crossed products: homological and K-theoretic to group actions. Kenneth Brown presents the "modern" theory of Noetherian rings and localization. These contributions as well as the others not presented here show that ring theory remains a vigorous and useful area. The planning and organization of the program were done by the under signed and the late Robert Warfield. His illness prevented his attendance at the meeting. It is to him we dedicate this volume. The organizers wish to extend their thanks to Irving Kaplansky, Director of MSRI, and the staff for all of their efforts in making this conference such a success. Susan Montgomery Lance Small vii NONCOMMUTATIVE RINGS TABLE OF CONTENTS PREFACE. . . . . . . . . . . . . . . . . . . . . . .. . . . Vll . . . . . . . . . . K. A. Brown THE REPRESENTATION THEORY OF NOETHERIAN RINGS 1 A. Joseph SOME RING THEORETIC TECHNIQUES AND OPEN PROBLEMS IN ENVELOPING ALGEBRAS. . . . . . . . . . . 27 . . . M. Lorenz CROSSED PRODUCTS: CHARACTERS, CYCLIC HOMOLOGY, AND GROTHENDIECK GROUPS . . . . . . . . . . . . . . . 69 . . . . . .

Noncommutative Noetherian Rings

John C. McConnell,James Christopher Robson,Lance W. Small
Noncommutative Noetherian Rings Book PDF

Author : John C. McConnell,James Christopher Robson,Lance W. Small
Publisher : American Mathematical Soc.
Page : 658 pages
File Size : 50,8 Mb
Release : 2001
Category : Noetherian rings
ISBN : 9780821821695

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Noncommutative Noetherian Rings by John C. McConnell,James Christopher Robson,Lance W. Small Pdf

This is a reprinted edition of a work that was considered the definitive account in the subject area upon its initial publication by J. Wiley & Sons in 1987. It presents, within a wider context, a comprehensive account of noncommutative Noetherian rings. The author covers the major developments from the 1950s, stemming from Goldie's theorem and onward, including applications to group rings, enveloping algebras of Lie algebras, PI rings, differential operators, and localization theory. The book is not restricted to Noetherian rings, but discusses wider classes of rings where the methods apply more generally. In the current edition, some errors were corrected, a number of arguments have been expanded, and the references were brought up to date. This reprinted edition will continue to be a valuable and stimulating work for readers interested in ring theory and its applications to other areas of mathematics.

Noetherian Rings and Their Applications

Lance W. Small
Noetherian Rings and Their Applications Book PDF

Author : Lance W. Small
Publisher : American Mathematical Soc.
Page : 130 pages
File Size : 52,8 Mb
Release : 1987
Category : Mathematics
ISBN : 9780821815250

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Noetherian Rings and Their Applications by Lance W. Small Pdf

". T. Stafford -- The Goldie rank of a module " . R. Farkas -- Noetherian group rings: An exercise in creating folklore and intuition " . C. Jantzen -- Primitive ideals in the enveloping algebra of a semisimple Lie algebra " . J. Enright -- Representation theory of semisimple Lie algebras " .-E. Björk -- Filtered Noetherian rings " . Rentschler -- Primitive ideals in enveloping algebras.

An Introduction to Noncommutative Noetherian Rings

K. R. Goodearl,Robert B. Warfield
An Introduction to Noncommutative Noetherian Rings Book PDF

Author : K. R. Goodearl,Robert B. Warfield
Publisher : Cambridge University Press
Page : 372 pages
File Size : 45,8 Mb
Release : 2004-07-12
Category : Mathematics
ISBN : 0521545374

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An Introduction to Noncommutative Noetherian Rings by K. R. Goodearl,Robert B. Warfield Pdf

This introduction to noncommutative noetherian rings is intended to be accessible to anyone with a basic background in abstract algebra. It can be used as a second-year graduate text, or as a self-contained reference. Extensive explanatory discussion is given, and exercises are integrated throughout. This edition incorporates substantial revisions, particularly in the first third of the book, where the presentation has been changed to increase accessibility and topicality. New material includes the basic types of quantum groups, which then serve as test cases for the theory developed.

Introduction to Noncommutative Algebra

Matej Brešar
Introduction to Noncommutative Algebra Book PDF

Author : Matej Brešar
Publisher : Springer
Page : 227 pages
File Size : 47,9 Mb
Release : 2014-10-14
Category : Mathematics
ISBN : 9783319086934

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Introduction to Noncommutative Algebra by Matej Brešar Pdf

Providing an elementary introduction to noncommutative rings and algebras, this textbook begins with the classical theory of finite dimensional algebras. Only after this, modules, vector spaces over division rings, and tensor products are introduced and studied. This is followed by Jacobson's structure theory of rings. The final chapters treat free algebras, polynomial identities, and rings of quotients. Many of the results are not presented in their full generality. Rather, the emphasis is on clarity of exposition and simplicity of the proofs, with several being different from those in other texts on the subject. Prerequisites are kept to a minimum, and new concepts are introduced gradually and are carefully motivated. Introduction to Noncommutative Algebra is therefore accessible to a wide mathematical audience. It is, however, primarily intended for beginning graduate and advanced undergraduate students encountering noncommutative algebra for the first time.

A First Course in Noncommutative Rings

T.Y. Lam
A First Course in Noncommutative Rings Book PDF

Author : T.Y. Lam
Publisher : Springer Science & Business Media
Page : 410 pages
File Size : 46,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468404067

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A First Course in Noncommutative Rings by T.Y. Lam Pdf

One of my favorite graduate courses at Berkeley is Math 251, a one-semester course in ring theory offered to second-year level graduate students. I taught this course in the Fall of 1983, and more recently in the Spring of 1990, both times focusing on the theory of noncommutative rings. This book is an outgrowth of my lectures in these two courses, and is intended for use by instructors and graduate students in a similar one-semester course in basic ring theory. Ring theory is a subject of central importance in algebra. Historically, some of the major discoveries in ring theory have helped shape the course of development of modern abstract algebra. Today, ring theory is a fer tile meeting ground for group theory (group rings), representation theory (modules), functional analysis (operator algebras), Lie theory (enveloping algebras), algebraic geometry (finitely generated algebras, differential op erators, invariant theory), arithmetic (orders, Brauer groups), universal algebra (varieties of rings), and homological algebra (cohomology of rings, projective modules, Grothendieck and higher K-groups). In view of these basic connections between ring theory and other branches of mathemat ics, it is perhaps no exaggeration to say that a course in ring theory is an indispensable part of the education for any fledgling algebraist. The purpose of my lectures was to give a general introduction to the theory of rings, building on what the students have learned from a stan dard first-year graduate course in abstract algebra.

Algebra II

A.I. Kostrikin,I.R. Shafarevich
Algebra II Book PDF

Author : A.I. Kostrikin,I.R. Shafarevich
Publisher : Springer Science & Business Media
Page : 241 pages
File Size : 55,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642728990

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Algebra II by A.I. Kostrikin,I.R. Shafarevich Pdf

The algebra of square matrices of size n ~ 2 over the field of complex numbers is, evidently, the best-known example of a non-commutative alge 1 bra • Subalgebras and subrings of this algebra (for example, the ring of n x n matrices with integral entries) arise naturally in many areas of mathemat ics. Historically however, the study of matrix algebras was preceded by the discovery of quatemions which, introduced in 1843 by Hamilton, found ap plications in the classical mechanics of the past century. Later it turned out that quaternion analysis had important applications in field theory. The al gebra of quaternions has become one of the classical mathematical objects; it is used, for instance, in algebra, geometry and topology. We will briefly focus on other examples of non-commutative rings and algebras which arise naturally in mathematics and in mathematical physics. The exterior algebra (or Grassmann algebra) is widely used in differential geometry - for example, in geometric theory of integration. Clifford algebras, which include exterior algebras as a special case, have applications in rep resentation theory and in algebraic topology. The Weyl algebra (Le. algebra of differential operators with· polynomial coefficients) often appears in the representation theory of Lie algebras. In recent years modules over the Weyl algebra and sheaves of such modules became the foundation of the so-called microlocal analysis. The theory of operator algebras (Le.

Abelian Groups and Noncommutative Rings: A Collection of Papers in Memory of Robert B. Warfield, Jr.

László Fuchs
Abelian Groups and Noncommutative Rings A Collection of Papers in Memory of Robert B Warfield Jr Book PDF

Author : László Fuchs
Publisher : American Mathematical Soc.
Page : 408 pages
File Size : 50,5 Mb
Release : 1992
Category : Mathematics
ISBN : 9780821851425

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Abelian Groups and Noncommutative Rings: A Collection of Papers in Memory of Robert B. Warfield, Jr. by László Fuchs Pdf

This collection of research papers is dedicated to the memory of the distinguished algebraist Robert B. Warfield, Jr. Focusing on abelian group theory and noncommutative ring theory, the book covers a wide range of topics reflecting Warfield's interests and includes two articles surveying his contributions to mathematics. Because the articles have been refereed to high standards and will not appear elsewhere, this volume is indispensable to any researcher in noncommutative ring theory or abelian group theory. With papers by some of the major leaders in the field, this book will also be important to anyone interested in these areas, as it provides an overview of current research directions.

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 : 50,6 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."

Topics in Non-Commutative Geometry

Y. Manin
Topics in Non Commutative Geometry Book PDF

Author : Y. Manin
Publisher : Princeton University Press
Page : 173 pages
File Size : 42,7 Mb
Release : 2014-07-14
Category : Mathematics
ISBN : 9781400862511

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Topics in Non-Commutative Geometry by Y. Manin Pdf

There is a well-known correspondence between the objects of algebra and geometry: a space gives rise to a function algebra; a vector bundle over the space corresponds to a projective module over this algebra; cohomology can be read off the de Rham complex; and so on. In this book Yuri Manin addresses a variety of instances in which the application of commutative algebra cannot be used to describe geometric objects, emphasizing the recent upsurge of activity in studying noncommutative rings as if they were function rings on "noncommutative spaces." Manin begins by summarizing and giving examples of some of the ideas that led to the new concepts of noncommutative geometry, such as Connes' noncommutative de Rham complex, supergeometry, and quantum groups. He then discusses supersymmetric algebraic curves that arose in connection with superstring theory; examines superhomogeneous spaces, their Schubert cells, and superanalogues of Weyl groups; and provides an introduction to quantum groups. This book is intended for mathematicians and physicists with some background in Lie groups and complex geometry. Originally published in 1991. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.