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Author : Jonathan S. Golan
Publisher : CRC Press
Page : 352 pages
File Size : 44,6 Mb
Release : 1975-01-01
Category : Mathematics
ISBN : 0824761987
Author : Bruno J. Mueller
Publisher : Unknown
Page : 88 pages
File Size : 54,5 Mb
Release : 1975
Category : Noncommutative rings
ISBN : UTEXAS:059173023338791
Author : Andrew Ranicki
Publisher : Cambridge University Press
Page : 332 pages
File Size : 49,5 Mb
Release : 2006-02-09
Category : Mathematics
ISBN : 052168160X
Noncommutative localization is a powerful algebraic technique for constructing new rings by inverting elements, matrices and more generally morphisms of modules. Originally conceived by algebraists (notably P. M. Cohn), it is now an important tool not only in pure algebra but also in the topology of non-simply-connected spaces, algebraic geometry and noncommutative geometry. This volume consists of 9 articles on noncommutative localization in algebra and topology by J. A. Beachy, P. M. Cohn, W. G. Dwyer, P. A. Linnell, A. Neeman, A. A. Ranicki, H. Reich, D. Sheiham and Z. Skoda. The articles include basic definitions, surveys, historical background and applications, as well as presenting new results. The book is an introduction to the subject, an account of the state of the art, and also provides many references for further material. It is suitable for graduate students and more advanced researchers in both algebra and topology.
Author : Susan Montgomery,Lance Small
Publisher : Springer Science & Business Media
Page : 182 pages
File Size : 52,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461397366
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 . . . . . .
Author : Surender K. Jain,Sergio R. Lopez-Permouth
Publisher : Springer
Page : 173 pages
File Size : 53,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540467458
The papers of this volume share as a common goal the structure and classi- fication of noncommutative rings and their modules, and deal with topics of current research including: localization, serial rings, perfect endomorphism rings, quantum groups, Morita contexts, generalizations of injectivitiy, and Cartan matrices.
Author : K. R. Goodearl,Robert B. Warfield
Publisher : Cambridge University Press
Page : 372 pages
File Size : 51,9 Mb
Release : 2004-07-12
Category : Mathematics
ISBN : 0521545374
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.
Author : Surender K. Jain,Sergio R. Lopez-Permouth
Publisher : Springer
Page : 168 pages
File Size : 50,6 Mb
Release : 1990-10-24
Category : Mathematics
ISBN : 3540531645
The papers of this volume share as a common goal the structure and classi- fication of noncommutative rings and their modules, and deal with topics of current research including: localization, serial rings, perfect endomorphism rings, quantum groups, Morita contexts, generalizations of injectivitiy, and Cartan matrices.
Author : A. V. Jategaonkar
Publisher : Cambridge University Press
Page : 341 pages
File Size : 43,5 Mb
Release : 1986-03-13
Category : Mathematics
ISBN : 9780521317139
This monograph first published in 1986 is a reasonably self-contained account of a large part of the theory of non-commutative Noetherian rings. The author focuses on two important aspects: localization and the structure of infective modules. The former is presented in the opening chapters after which some new module-theoretic concepts and methods are used to formulate a new view of localization. This view, which is one of the book's highlights, shows that the study of localization is inextricably linked to the study of certain injectives and leads, for the first time, to some genuine applications of localization in the study of Noetherian rings. In the last part Professor Jategaonkar introduces a unified setting for four intensively studied classes of Noetherian rings: HNP rings, PI rings, enveloping algebras of solvable Lie algebras, and group rings of polycyclic groups. Some appendices summarize relevant background information about these four classes.
Author : J.H. Cozzens,F.L. Sandomierski
Publisher : Springer
Page : 221 pages
File Size : 54,5 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540379836
Author : K. R. Goodearl,Robert B. Warfield
Publisher : Cambridge University Press
Page : 328 pages
File Size : 40,7 Mb
Release : 1989
Category : Mathematics
ISBN : 0521369258
Introduces and applies the standard techniques in the area (ring of fractions, bimodules, Krull dimension, linked prime ideals).
Author : T.Y. Lam
Publisher : Springer Science & Business Media
Page : 410 pages
File Size : 41,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468404067
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.
Author : Sergio R. López-Permouth,Jae Keol Park,S. Tariq Rizvi,Cosmin S. Roman
Publisher : American Mathematical Soc.
Page : 283 pages
File Size : 45,9 Mb
Release : 2018-09-06
Category : Modules (Algebra)
ISBN : 9781470435554
This volume, dedicated to Bruno J. Müller, a renowned algebraist, is a collection of papers that provide a snapshot of the diversity of themes and applications that interest algebraists today. The papers highlight the latest progress in ring and module research and present work done on the frontiers of the topics discussed. In addition, selected expository articles are included to give algebraists and other mathematicians, including graduate students, an accessible introduction to areas that may be outside their own expertise.
Author : Tsit-Yuen Lam
Publisher : Springer Science & Business Media
Page : 577 pages
File Size : 51,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461205258
This new book can be read independently from the first volume and may be used for lecturing, seminar- and self-study, or for general reference. It focuses more on specific topics in order to introduce readers to a wealth of basic and useful ideas without the hindrance of heavy machinery or undue abstractions. User-friendly with its abundance of examples illustrating the theory at virtually every step, the volume contains a large number of carefully chosen exercises to provide newcomers with practice, while offering a rich additional source of information to experts. A direct approach is used in order to present the material in an efficient and economic way, thereby introducing readers to a considerable amount of interesting ring theory without being dragged through endless preparatory material.
Author : P. J. Fleury
Publisher : Springer
Page : 152 pages
File Size : 52,7 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540393719
Author : John C. McConnell,James Christopher Robson,Lance W. Small
Publisher : American Mathematical Soc.
Page : 658 pages
File Size : 55,8 Mb
Release : 2001
Category : Mathematics
ISBN : 9780821821695
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.