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Exercises in Modules and Rings / Edition 1

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Overview

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.

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Editorial Reviews

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"This volume, a companion for the author’s graduate-level textbook … consists of a complete set of solutions to all … . should be on the bookshelf of every serious graduate student in theoretical mathematics. As one expects from the author, the writing in this book is clear and precise, and some of the problem solutions (and counterexamples to conjectures) presented are quite elegant." (Jonathan Golan, Mathematical Reviews, Issue 2007 h)

"Exercises in Classical Ring Theory is an outgrowth of the author’s lectures on noncommutative rings given at Berkeley. The book presents solutions to over 400 exercises … . Those who purchase the book should find it helpful in the problem solving process as well as a demonstration of the different applications of theorems from ring theory." (Paul E. Bland, Zentralblatt MATH, Vol. 1121 (23), 2007)

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Product Details

  • ISBN-13: 9781441931757
  • Publisher: Springer New York
  • Publication date: 11/19/2010
  • Series: Problem Books in Mathematics Series
  • Edition description: Softcover reprint of hardcover 1st ed. 2007
  • Edition number: 1
  • Pages: 414
  • Product dimensions: 9.21 (w) x 6.14 (h) x 0.88 (d)

Table of Contents

Free Modules.- Projective and Injective Modules.- Flat Modules and Homological Dimensions.- More Theory of Modules.- Rings of Quotients.- More Rings of Quotients.- Frobenius and Quasi-Frobenius Rings.- Matrix Rings, Categories of Modules, and Morita Theory.

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