**Graduate Studies in Mathematics**

Volume: 91;
2008;
648 pp;
Hardcover

MSC: Primary 16; 17;
Secondary 20

Print ISBN: 978-0-8218-4153-2

Product Code: GSM/91

List Price: $89.00

Individual Member Price: $71.20

**Electronic ISBN: 978-1-4704-1802-1
Product Code: GSM/91.E**

List Price: $89.00

Individual Member Price: $71.20

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#### Supplemental Materials

# Graduate Algebra: Noncommutative View

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*Louis Halle Rowen*

This book is a companion volume to *Graduate Algebra: Commutative
View* (published as volume 73 in this series). The main and most important
feature of the book is that it presents a unified approach to many
important topics, such as group theory, ring theory, Lie algebras, and
gives conceptual proofs of many basic results of noncommutative algebra.
There are also a number of major results in noncommutative algebra that
are usually found only in technical works, such as Zelmanov's proof of the
restricted Burnside problem in group theory, word problems in groups,
Tits's alternative in algebraic groups, PI algebras, and many of the roles
that Coxeter diagrams play in algebra.

The first half of the book can serve as a one-semester course on
noncommutative algebra, whereas the remaining part of the book describes
some of the major directions of research in the past 100 years. The main
text is extended through several appendices, which permits the inclusion
of more advanced material, and numerous exercises. The only prerequisite
for using the book is an undergraduate course in algebra; whenever
necessary, results are quoted from *Graduate Algebra: Commutative
View*.

#### Table of Contents

# Table of Contents

## Graduate Algebra: Noncommutative View

- Cover Cover11 free
- Title page iii5 free
- Contents vii9 free
- Introduction xiii15 free
- List of symbols xvii19 free
- Prerequisites xxiii25 free
- Part IV. The structure of rings 129 free
- Introduction to the structure of rings 331
- Fundamental concepts in ring theory 533
- Semisimple modules and rings and the Wedderburn-Artin theorem 3361
- The Jacobson program applied to left Artinian rings 4573
- Noetherian rings and the role of prime rings 6391
- Algebras in terms of generators and relations 87115
- Tensor products 137165
- Exercises–Part IV 161189
- Part V. Representations of groups and Lie algebras 193221
- Introduction to representations of groups and Lie algebras 195223
- Group representations and group algebras 197225
- Characters of finite groups 249277
- Lie algebras and other nonassociative algebras 271299
- Dynkin diagrams (Coxeter-Dynkin graphs and Coxeter groups) 337365
- Exercises–Part V 355383
- Part VI. Representable algebras 401429
- Introduction to representable algebras 403431
- Polynomial identities and representable algebras 405433
- Central simple algebras and the Brauer group 447475
- Homological algebra and categories of modules 485513
- Hopf algebras 547575
- Exercises–Part VI 563591
- List of major results 599627
- Bibliography 627655
- List of names 635663
- Index 637665 free
- Back Cover Back Cover1683

#### Readership

Graduate students and research mathematicians interested in various topics of noncommutative algebra.

#### Reviews

Each part ends with more than 30 pages of exercises, from the basic to the challenging, carefully arranged and labeled according to the chapter (or appendix) to which they related ... a striking and very enjoyable feature of the book is the huge number of digressions: there are frequent pauses to point out noteworthy aspects of the terrain which lies ahead, beyond what can be covered in detail in a book of this sort. The style, layout and precision of the book make it a pleasure to read...

-- Mathematical Reviews

The book is largely self-contained. ...a valuable textbook and a reliable reference for graduate students.

-- MAA Reviews