**AMS Chelsea Publishing**

Volume: 348;
2004;
306 pp;
Hardcover

MSC: Primary 16;
Secondary 19

Print ISBN: 978-0-8218-3680-4

Product Code: CHEL/348.H

List Price: $50.00

Individual Member Price: $45.00

**Electronic ISBN: 978-1-4704-2999-7
Product Code: CHEL/348.H.E**

List Price: $50.00

Individual Member Price: $45.00

#### Supplemental Materials

# A Course in Ring Theory

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*Donald S. Passman*

First published in 1991, this book contains the core material for an
undergraduate first course in ring theory. Using the underlying theme of
projective and injective modules, the author touches upon various aspects of
commutative and noncommutative ring theory. In particular, a number of major
results are highlighted and proved.

Part I, "Projective Modules", begins with basic
module theory and then proceeds to surveying various special classes of rings
(Wedderburn, Artinian and Noetherian rings, hereditary rings, Dedekind domains,
etc.). This part concludes with an introduction and discussion of the concepts
of the projective dimension.

Part II, "Polynomial Rings", studies these rings in a mildly noncommutative
setting. Some of the results proved include the Hilbert Syzygy Theorem (in the
commutative case) and the Hilbert Nullstellensatz (for almost commutative
rings).

Part III, "Injective Modules", includes, in particular, various notions of the
ring of quotients, the Goldie Theorems, and the characterization of the
injective modules over Noetherian rings.

The book contains numerous exercises and a list of suggested additional
reading. It is suitable for graduate students and researchers interested in
ring theory.

#### Table of Contents

# Table of Contents

## A Course in Ring Theory

- Cover Cover11
- Title page iii4
- Preface v6
- Contents vii8
- Projective modules 110
- Modules and homomorphisms 312
- Projective modules 1322
- Completely reducible modules 2332
- Wedderburn rings 3342
- Artinian rings 4453
- Hereditary rings 5665
- Dedekind domains 6473
- Projective dimension 7483
- Tensor products 8493
- Local rings 95104
- Polynomial rings 103112
- Skew polynomial rings 105114
- Grothendieck groups 115124
- Graded rings and modules 124133
- Induced modules 133142
- Syzygy theorem 142151
- Patching theorem 152161
- Serre conjecture 161170
- Big projectives 171180
- Generic flatness 180189
- Nullstellensatz 190199
- Injective modules 201210
- Injective modules 203212
- Injective dimension 213222
- Essential extensions 223232
- Maximal ring of quotients 233242
- Classical ring of quotients 242251
- Goldie rings 252261
- Uniform dimension 262271
- Uniform injective modules 273282
- Reduced rank 284293
- Index 295304
- Back Cover Back Cover1322

#### Readership

Graduate students and research mathematicians interested in ring theory.

#### Reviews

"There seems to be an emerging consensus as to what material should constitute the core of a first course in module-theoretic ring theory ... The book ... is definitely within the bounds of that consensus ... presentation is clear, the proofs are often quite ingenious and the exercises are well chosen ... definitely suitable for use as a textbook."

-- Mathematical Reviews

This excellently written book, which has been published originally by Wadsworthand Brooks in 1991, is already a classic ... A book recommendable now as before!

-- Monatshefte für Mathematik