**Graduate Studies in Mathematics**

Volume: 180;
2017;
558 pp;
Hardcover

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

Print ISBN: 978-1-4704-2311-7

Product Code: GSM/180

List Price: $94.00

AMS Member Price: $75.20

MAA Member Price: $84.60

**Electronic ISBN: 978-1-4704-4170-8
Product Code: GSM/180.E**

List Price: $94.00

AMS Member Price: $75.20

MAA Member Price: $84.60

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#### Supplemental Materials

# Advanced Modern Algebra: Third Edition, Part 2

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*Joseph J. Rotman*

This book is the second part of the new edition of Advanced Modern Algebra (the first part published as Graduate Studies in Mathematics, Volume 165). Compared to the previous edition, the material has been significantly reorganized and many sections have been rewritten. The book presents many topics mentioned in the first part in greater depth and in more detail. The five chapters of the book are devoted to group theory, representation theory, homological algebra, categories, and commutative algebra, respectively. The book can be used as a text for a second abstract algebra graduate course, as a source of additional material to a first abstract algebra graduate course, or for self-study.

#### Readership

Graduate students and researchers interested in learning and teaching algebra.

#### Reviews & Endorsements

This is a good book and a fitting tribute to a great mathematical expositor. I'll keep both the second edition and the two parts of the third edition on my shelf, and I'm sure I'll turn to them often in the future.

-- Fernando Q. Gouvêa, MAA Reviews

#### Table of Contents

# Table of Contents

## Advanced Modern Algebra: Third Edition, Part 2

- Cover Cover11
- Title page i2
- Contents iii4
- Foreword vii8
- Preface to Third Edition: Part 2 ix10
- Chapter C-1. More Groups 112
- C-1.1. Group Actions 112
- C-1.2. Sylow Theorems 2435
- C-1.3. Solvable and Nilpotent Groups 3344
- C-1.4. Projective Unimodular Groups 5061
- C-1.5. More Group Actions 6677
- C-1.6. Free Groups and Presentations 8192
- C-1.7. Nielsen–Schreier Theorem 97108
- C-1.8. The Baer–Levi Proof 102113
- C-1.9. Free Products and the Kurosh Theorem 118129
- C-1.10. Epilog 124135

- Chapter C-2. Representation Theory 127138
- C-2.1. Artinian and Noetherian 127138
- C-2.2. Jacobson Radical 130141
- C-2.3. Group Actions on Modules 135146
- C-2.4. Semisimple Rings 137148
- C-2.5. Wedderburn–Artin Theorems 146157
- C-2.6. Introduction to Lie Algebras 161172
- C-2.7. Characters 168179
- C-2.8. Class Functions 176187
- C-2.9. Character Tables and Orthogonality Relations 180191
- C-2.10. Induced Characters 186197
- C-2.11. Algebraic Integers Interlude 193204
- C-2.12. Theorems of Burnside and of Frobenius 200211
- C-2.13. Division Algebras 208219

- Chapter C-3. Homology 223234
- C-3.1. Introduction 223234
- C-3.2. Semidirect Products 226237
- C-3.3. General Extensions and Cohomology 236247
- C-3.4. Complexes 255266
- C-3.5. Homology Functors 262273
- C-3.6. Derived Functors 271282
- C-3.7. Right Derived Functors 285296
- C-3.8. Ext and Tor 292303
- C-3.9. Cohomology of Groups 309320
- C-3.10. Crossed Products 326337
- C-3.11. Introduction to Spectral Sequences 333344

- Chapter C-4. More Categories 339350
- Chapter C-5. Commutative Rings III 419430
- Bibliography 527538
- Index 537548
- Back Cover Back Cover1570