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Louis Halle Rowen Bar-Ilan University, Ramat Gan, Israel
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Hardcover ISBN: 978-0-8218-4153-2
Product Code: GSM/91
List Price: $95.00 MAA Member Price:$85.50
AMS Member Price: $76.00 Electronic ISBN: 978-1-4704-1802-1 Product Code: GSM/91.E List Price:$89.00
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AMS Member Price: $114.00 Click above image for expanded view Graduate Algebra: Noncommutative View Louis Halle Rowen Bar-Ilan University, Ramat Gan, Israel Available Formats:  Hardcover ISBN: 978-0-8218-4153-2 Product Code: GSM/91  List Price:$95.00 MAA Member Price: $85.50 AMS Member Price:$76.00
 Electronic ISBN: 978-1-4704-1802-1 Product Code: GSM/91.E
 List Price: $89.00 MAA Member Price:$80.10 AMS Member Price: $71.20 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$142.50 MAA Member Price: $128.25 AMS Member Price:$114.00
• Book Details

Volume: 912008; 648 pp
MSC: Primary 16; 17; Secondary 20;

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.

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

• Part IV. The structure of rings
• Introduction to the structure of rings
• Chapter 13. Fundamental concepts in ring theory
• Chapter 14. Semisimple modules and rings and the Wedderburn-Artin theorem
• Chapter 15. The Jacobson program applied to left Artinian rings
• Chapter 16. Noetherian rings and the role of prime rings
• Chapter 17. Algebras in terms of generators and relations
• Chapter 18. Tensor products
• Exercises—Part IV
• Part V. Representations of groups and Lie algebras
• Introduction to representations of groups and Lie algebras
• Chapter 19. Group representations and group algebras
• Chapter 20. Characters of finite groups
• Chapter 21. Lie algebras and other nonassociative algebras
• Chapter 22. Dynkin diagrams (Coxeter-Dynkin graphs and Coxeter groups)
• Exercises—Part V
• Part VI. Representable algebras
• Introduction to representable algebras
• Chapter 23. Polynomial identities and representable algebras
• Chapter 24. Central simple algebras and the Brauer group
• Chapter 25. Homological algebra and categories of modules
• Chapter 26. Hopf algebras
• Exercises—Part VI

• 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
• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 912008; 648 pp
MSC: Primary 16; 17; Secondary 20;

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.

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

• Part IV. The structure of rings
• Introduction to the structure of rings
• Chapter 13. Fundamental concepts in ring theory
• Chapter 14. Semisimple modules and rings and the Wedderburn-Artin theorem
• Chapter 15. The Jacobson program applied to left Artinian rings
• Chapter 16. Noetherian rings and the role of prime rings
• Chapter 17. Algebras in terms of generators and relations
• Chapter 18. Tensor products
• Exercises—Part IV
• Part V. Representations of groups and Lie algebras
• Introduction to representations of groups and Lie algebras
• Chapter 19. Group representations and group algebras
• Chapter 20. Characters of finite groups
• Chapter 21. Lie algebras and other nonassociative algebras
• Chapter 22. Dynkin diagrams (Coxeter-Dynkin graphs and Coxeter groups)
• Exercises—Part V
• Part VI. Representable algebras
• Introduction to representable algebras
• Chapter 23. Polynomial identities and representable algebras
• Chapter 24. Central simple algebras and the Brauer group
• Chapter 25. Homological algebra and categories of modules
• Chapter 26. Hopf algebras
• Exercises—Part VI
• 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
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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