Exercises In Modules And Rings
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Exercises In Modules And Rings
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Author : T.Y. Lam
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-12-08
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 2009-12-08 with Mathematics categories.
The idea of writing this book came roughly at the time of publication of my graduate text Lectures on Modules and Rings, Springer GTM Vol. 189, 1999. Since that time, teaching obligations and intermittent intervention of other projects caused prolonged delays in the work on this volume. Only a lucky break in my schedule in 2006 enabled me to put the finishing touches on the completion of this long overdue book. This book is intended to serve a dual purpose. First, it is designed as a "problem book" for Lectures. As such, it contains the statements and full solutions of the many exercises that appeared in Lectures. Second, this book is also offered as a reference and repository for general information in the theory of modules and rings that may be hard to find in the standard textbooks in the field. As a companion volume to Lectures, this work covers the same math ematical material as its parent work; namely, the part of ring theory that makes substantial use of the notion of modules. The two books thus share the same table of contents, with the first half treating projective, injective, and flat modules, homological and uniform dimensions, and the second half dealing with noncommutative localizations and Goldie's theorems, maximal rings of quotients, Frobenius and quasi-Frobenius rings, conclud ing with Morita's theory of category equivalences and dualities.
Lectures On Modules And Rings
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Author : Tsit-Yuen Lam
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Lectures On Modules And Rings written by Tsit-Yuen 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 2012-12-06 with Mathematics categories.
Textbook writing must be one of the cruelest of self-inflicted tortures. - Carl Faith Math Reviews 54: 5281 So why didn't I heed the warning of a wise colleague, especially one who is a great expert in the subject of modules and rings? The answer is simple: I did not learn about it until it was too late! My writing project in ring theory started in 1983 after I taught a year-long course in the subject at Berkeley. My original plan was to write up my lectures and publish them as a graduate text in a couple of years. My hopes of carrying out this plan on schedule were, however, quickly dashed as I began to realize how much material was at hand and how little time I had at my disposal. As the years went by, I added further material to my notes, and used them to teach different versions of the course. Eventually, I came to the realization that writing a single volume would not fully accomplish my original goal of giving a comprehensive treatment of basic ring theory. At the suggestion of Ulrike Schmickler-Hirzebruch, then Mathematics Editor of Springer-Verlag, I completed the first part of my project and published the write up in 1991 as A First Course in Noncommutative Rings, GTM 131, hereafter referred to as First Course (or simply FC).
Exercises In Classical Ring Theory
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Author : T.Y. Lam
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Exercises In Classical Ring Theory 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 2013-06-29 with Mathematics categories.
Based in large part on the comprehensive "First Course in Ring Theory" by the same author, this book provides a comprehensive set of problems and solutions in ring theory that will serve not only as a teaching aid to instructors using that book, but also for students, who will see how ring theory theorems are applied to solving ring-theoretic problems and how good proofs are written. The author demonstrates that problem-solving is a lively process: in "Comments" following many solutions he discusses what happens if a hypothesis is removed, whether the exercise can be further generalized, what would be a concrete example for the exercise, and so forth. The book is thus much more than a solution manual.
Rings And Categories Of Modules
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Author : Frank W. Anderson
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Rings And Categories Of Modules written by Frank W. Anderson 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 2012-12-06 with Mathematics categories.
This book is intended to provide a reasonably self-contained account of a major portion of the general theory of rings and modules suitable as a text for introductory and more advanced graduate courses. We assume the famil iarity with rings usually acquired in standard undergraduate algebra courses. Our general approach is categorical rather than arithmetical. The continuing theme of the text is the study of the relationship between the one-sided ideal structure that a ring may possess and the behavior of its categories of modules. Following a brief outline of set-theoretic and categorical foundations, the text begins with the basic definitions and properties of rings, modules and homomorphisms and ranges through comprehensive treatments of direct sums, finiteness conditions, the Wedderburn-Artin Theorem, the Jacobson radical, the hom and tensor functions, Morita equivalence and duality, de composition theory of injective and projective modules, and semi perfect and perfect rings. In this second edition we have included a chapter containing many of the classical results on artinian rings that have hdped to form the foundation for much of the contemporary research on the representation theory of artinian rings and finite dimensional algebras. Both to illustrate the text and to extend it we have included a substantial number of exercises covering a wide spectrum of difficulty. There are, of course" many important areas of ring and module theory that the text does not touch upon.
Lectures On Modules And Rings
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Author : Tsit-Yuen Lam
language : en
Publisher: Springer Science & Business Media
Release Date : 1999
Lectures On Modules And Rings written by Tsit-Yuen 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 1999 with Mathematics categories.
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.
Foundations Of Module And Ring Theory
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Author : Robert Wisbauer
language : en
Publisher: Routledge
Release Date : 2018-05-11
Foundations Of Module And Ring Theory written by Robert Wisbauer and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-11 with Mathematics categories.
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. It is a useful and stimulating study for those new to the subject as well as for researchers and serves as a reference volume. Starting form a basic understanding of linear algebra, the theory is presented and accompanied by complete proofs. For a module M, the smallest Grothendieck category containing it is denoted by o[M] and module theory is developed in this category. Developing the techniques in o[M] is no more complicated than in full module categories and the higher generality yields significant advantages: for example, module theory may be developed for rings without units and also for non-associative rings. Numerous exercises are included in this volume to give further insight into the topics covered and to draw attention to related results in the literature.
Rings And Their Modules
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Author : Paul E. Bland
language : en
Publisher: Walter de Gruyter
Release Date : 2011
Rings And Their Modules written by Paul E. Bland 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 2011 with Mathematics categories.
This book is an introduction to the theory of rings and modules that goes beyond what one normally obtains in a graduate course in abstract algebra. In addition to the presentation of standard topics in ring and module theory, it also covers category theory, homological algebra and even more specialized topics like injective envelopes and proj
Ring And Module Theory
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Author : Toma Albu
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-02-04
Ring And Module Theory written by Toma Albu 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 2011-02-04 with Mathematics categories.
This book is a collection of invited papers and articles, many presented at the 2008 International Conference on Ring and Module Theory. The papers explore the latest in various areas of algebra, including ring theory, module theory and commutative algebra.
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.
An Introduction To Rings And Modules
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Author : A. J. Berrick
language : en
Publisher: Cambridge University Press
Release Date : 2000-05
An Introduction To Rings And Modules written by A. J. Berrick and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-05 with Mathematics categories.
This is a concise 2000 introduction at graduate level to ring theory, module theory and number theory.