A Course in Ring Theory

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Overview

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

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Editorial Reviews

Booknews
A textbook presenting a module theoretic approach to various aspects of commutative and noncommutative ring theory, for students familiar with basic ring theory concepts such as ideals and homomorphisms, but not necessarily with modules. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780821836804
  • Publisher: American Mathematical Society
  • Publication date: 9/28/2004
  • Series: AMS Chelsea Publishing Series , #348
  • Edition description: New Edition
  • Pages: 306
  • Product dimensions: 7.20 (w) x 10.20 (h) x 0.90 (d)

Table of Contents

1 Modules and homomorphisms 3
2 Projective modules 13
3 Completely reducible modules 23
4 Wedderburn rings 33
5 Artinian rings 44
6 Hereditary rings 56
7 Dedekind domains 64
8 Projective dimension 74
9 Tensor products 84
10 Local rings 95
11 Skew polynomial rings 105
12 Grothendieck groups 115
13 Graded rings and modules 124
14 Induced modules 133
15 Syzygy theorem 142
16 Patching theorem 152
17 Serre conjecture 161
18 Big projectives 171
19 Generic flatness 180
20 Nullstellensatz 190
21 Injective modules 203
22 Injective dimension 213
23 Essential extensions 223
24 Maximal ring of quotients 233
25 Classical ring of quotients 242
26 Goldie rings 252
27 Uniform dimension 262
28 Uniform injective modules 273
29 Reduced rank 284
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