**Graduate Studies in Mathematics**

Volume: 165;
2015;
706 pp;
Hardcover

MSC: Primary 12; 13; 14; 15; 16; 18; 20;

Print ISBN: 978-1-4704-1554-9

Product Code: GSM/165

List Price: $89.00

AMS Member Price: $71.20

MAA Member Price: $80.10

**Electronic ISBN: 978-1-4704-2731-3
Product Code: GSM/165.E**

List Price: $89.00

AMS Member Price: $71.20

MAA Member Price: $80.10

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#### Supplemental Materials

# Advanced Modern Algebra: Third Edition, Part 1

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*Joseph J. Rotman*

This new edition, now in two parts, has been significantly reorganized and many sections have been rewritten. This first part, designed for a first year of graduate algebra, consists of two courses: Galois theory and Module theory. Topics covered in the first course are classical formulas for solutions of cubic and quartic equations, classical number theory, commutative algebra, groups, and Galois theory. Topics in the second course are Zorn's lemma, canonical forms, inner product spaces, categories and limits, tensor products, projective, injective, and flat modules, multilinear algebra, affine varieties, and Gröbner bases.

#### Readership

Graduate students and researchers interested in learning and teaching algebra.

#### Reviews & Endorsements

The organization of the text is clear and the pace is leisurely...recently I taught the second part of a first-year graduate course in algebra, and in the process dipped into this book at various points. I enjoyed the presentation, and the commentary on constructions and results aimed to place them in context, and I found the numerous examples and exercises helpful. I will be using this book when teaching such courses again, if not always as the main text, certainly as a useful supplement.

-- Srikanth B. Iyengar, Mathematical Reviews

Rotman is a wonderful expositor, and the two courses in this book strike me as well thought out and well presented.

-- Fernando Q. Gouvêa, MAA

#### Table of Contents

# Table of Contents

## Advanced Modern Algebra: Third Edition, Part 1

- Cover Cover11
- Title page iii4
- Dedication v6
- Contents vii8
- Preface to the third edition: Volume I xi12
- Part A. Course I 116
- Chapter A-1. Classical formulas 318
- Chapter A-2. Classical number theory 924
- Chapter A-3. Commutative rings 2944
- Chapter A-4. Groups 115130
- Chapter A-5. Galois theory 179194
- Chapter A-6. Appendix: Set theory 235250
- Chapter A-7. Appendix: Linear Algebra 247262
- Part B. Course II 271286
- Chapter B-1. Modules 273288
- Chapter B-2. Zorn’s lemma 313328
- Chapter B-3. Advanced linear algebra 359374
- Chapter B-4. Categories of modules 441456
- Chapter B-5. Multilinear algebra 543558
- Chapter B-6. Commutative algebra II 591606
- Chapter B-7. Appendix: Categorical limits 651666
- Chapter B-8. Appendix: Topological spaces 673688
- Bibliography 681696
- Special notation 687702
- Index 693708
- Back Cover Back Cover1722