Exercises in Modules and Rings

1. Front Matter

   Pages i-xviii

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2. Free Modules, Projective, and Injective Modules

   • T. Y. Lam

   Pages 1-95

3. Flat Modules and Homological Dimensions

   • T. Y. Lam

   Pages 97-154

4. More Theory of Modules

   • T. Y. Lam

   Pages 155-216

5. Rings of Quotients

   • T. Y. Lam

   Pages 217-269

6. More Rings of Quotients

   • T. Y. Lam

   Pages 271-298

7. Frobenius and Quasi-Frobenius Rings

   • T. Y. Lam

   Pages 299-342

8. Matrix Rings, Categories of Modules and Morita Theory

   • T. Y. Lam

   Pages 343-402

9. Back Matter

   Pages 403-413

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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.

• Division
• Volume
• matrix

From the reviews:

"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)

• Department of Mathematics, University of California, Berkeley, Berkeley, USA

  T. Y. Lam

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