Exercises in Modules and Rings (eBook)

T.Y. Lam (Autor)

eBook Download: PDF

2009 | 2007
XVIII, 414 Seiten
Springer New York (Verlag)
978-0-387-48899-8 (ISBN)

Infos

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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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 "e;problem book"e; 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.

Inhalt

Preface 7
Contents 9
Notes to the Reader 11
Partial List of Notations 13
Partial List of Abbreviations 16
Chapter 1 Free Modules, Projective, and Injective Modules 18
Chapter 2 Flat Modules and Homological Dimensions 113
Chapter 3 More Theory of Modules 171
Chapter 4 Rings of Quotients 233
Chapter 5 More Rings of Quotients 286
Chapter 6 Frobenius and Quasi- Frobenius Rings 314
Chapter 7 Matrix Rings, Categories of Modules and Morita Theory 358
Name Index 418
Subject Index 421

Produkt-Details

• Erscheint lt. Verlag: 8.12.2009
• Reihe/Serie: Problem Books in Mathematics
• Reihe/Serie: Problem Books in Mathematics
• Zusatzinfo: XVIII, 414 p.
• Verlagsort: New York
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Technik
• Schlagworte: Division • Matrix • Volume
• ISBN-10: 0-387-48899-5 / 0387488995
• ISBN-13: 978-0-387-48899-8 / 9780387488998