Cyclic Modules And The Structure Of Rings
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Cyclic Modules And The Structure Of Rings
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Author : S. K. Jain
language : en
Publisher: Oxford University Press
Release Date : 2012-09-27
Cyclic Modules And The Structure Of Rings written by S. K. Jain and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-27 with Mathematics categories.
This unique and comprehensive volume provides an up-to-date account of the literature on the subject of determining the structure of rings over which cyclic modules or proper cyclic modules have a finiteness condition or a homological property. The finiteness conditions and homological properties are closely interrelated in the sense that either hypothesis induces the other in some form. This is the first book to bring all of this important material on the subject together. Over the last 25 years or more numerous mathematicians have investigated rings whose factor rings or factor modules have a finiteness condition or a homological property. They made important contributions leading to new directions and questions, which are listed at the end of each chapter for the benefit of future researchers. There is a wealth of material on the topic which is combined in this book, it contains more than 200 references and is not claimed to be exhaustive. This book will appeal to graduate students, researchers, and professionals in algebra with a knowledge of basic noncommutative ring theory, as well as module theory and homological algebra, equivalent to a one-year graduate course in the theory of rings and modules.
Cyclic Modules And The Structure Of Rings
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Author : S.K. Jain
language : en
Publisher: Oxford Mathematical Monographs
Release Date : 2012-09-27
Cyclic Modules And The Structure Of Rings written by S.K. Jain and has been published by Oxford Mathematical Monographs this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-27 with Mathematics categories.
This unique monograph brings together important material in the field of noncommutative rings and modules. It provides an up-to-date account of the topic of cyclic modules and the structure of rings which will be of particular interest to those working in abstract algebra and to graduate students who are exploring potential research topics.
Modules And The Structure Of Rings
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Author : Golan
language : en
Publisher: CRC Press
Release Date : 1991-04-24
Modules And The Structure Of Rings written by Golan and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-04-24 with Mathematics categories.
This book offers vital background information on methods for solving hard classification problems of algebraic structures. It explains how algebraists deal with the problem of the structure of modules over rings and how they make use of these structures to classify rings.
Foundations Of Module And Ring Theory
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Author : Robert Wisbauer
language : en
Publisher: CRC Press
Release Date : 1991-09-05
Foundations Of Module And Ring Theory written by Robert Wisbauer and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-09-05 with Mathematics categories.
Translated (with the addition of a number of new results, exercises, and references) from the German original of 1988 (Verlag Reinhard Fischer, Munich), this volume provides a comprehensive introduction to module theory and the related part of ring theory, including original results as well as the most recent work. Starting from a basic understanding of linear algebra, the theory is presented with complete proofs. For undergraduate, graduate, and research level mathematicians working in algebra, module, and ring theory. Annotation copyrighted by Book News, Inc., Portland, OR
Modules And Rings
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Author : David Alexander Ross Wallace
language : en
Publisher:
Release Date : 1982
Modules And Rings written by David Alexander Ross Wallace and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Mathematics categories.
Modules And The Structure Of Rings
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Author : Golan
language : en
Publisher: Routledge
Release Date : 2017-10-19
Modules And The Structure Of Rings written by Golan and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-19 with Mathematics categories.
This textbook is designed for students with at least one solid semester of abstract algebra,some linear algebra background, and no previous knowledge of module theory. Modulesand the Structure of Rings details the use of modules over a ring as a means of consideringthe structure of the ring itself--explaining the mathematics and "inductivereasoning" used in working on ring theory challenges and emphasizing modules insteadof rings.Stressing the inductive aspect of mathematical research underlying the formal deductivestyle of the literature, this volume offers vital background on current methods for solvinghard classification problems of algebraic structures. Written in an informal butcompletely rigorous style, Modules and the Structure of Rings clarifies sophisticatedproofs ... avoids the formalism of category theory ... aids independent study or seminarwork ... and supplies end-of-chapter problems.This book serves as an excellent primary.text for upper-level undergraduate and graduatestudents in one-semester courses on ring or module theory-laying a foundation formore advanced study of homological algebra or module theory.
Exercises In Modules And Rings
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Author : T.Y. Lam
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-12-15
Exercises In Modules And Rings written by T.Y. Lam and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-15 with Mathematics categories.
This volume offers a compendium of exercises of varying degree of difficulty in the theory of modules and rings. It is the companion volume to GTM 189. All exercises are solved in full detail. Each section begins with an introduction giving the general background and the theoretical basis for the problems that follow.
Extending Modules
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Author : Nguyen Viet Dung
language : en
Publisher: Routledge
Release Date : 2019-01-22
Extending Modules written by Nguyen Viet Dung and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-22 with Mathematics categories.
Module theory is an important tool for many different branches of mathematics, as well as being an interesting subject in its own right. Within module theory, the concept of injective modules is particularly important. Extending modules form a natural class of modules which is more general than the class of injective modules but retains many of its
Modules Over Discrete Valuation Domains
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Author : Piotr A. Krylov
language : en
Publisher: Walter de Gruyter
Release Date : 2008
Modules Over Discrete Valuation Domains written by Piotr A. Krylov and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
"In this book, modules over a specific class of rings, the discrete valuations domains, are considered. Such modules call for a special consideration, since they have specific properties and play an important role in various areas of algebra, especially of commutative algebra. The text is accompanied by exercises, historical remarks, links to related fields and open problems. It is useful for students, graduates studying algebra, young researchers, and experts."--BOOK JACKET.
Modules Over Discrete Valuation Rings
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Author : Piotr A. Krylov
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-09-24
Modules Over Discrete Valuation Rings written by Piotr A. Krylov and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-24 with Mathematics categories.
This book provides the first systematic treatment of modules over discrete valuation domains, which play an important role in various areas of algebra, especially in commutative algebra. Many important results representing the state of the art are presented in the text along with interesting open problems. This updated edition presents new approaches on p-adic integers and modules, and on the determinability of a module by its automorphism group. Contents Preliminaries Basic facts Endomorphism rings of divisible and complete modules Representation of rings by endomorphism rings Torsion-free modules Mixed modules Determinity of modules by their endomorphism rings Modules with many endomorphisms or automorphisms