Graduate Algebra: Noncommutative View (Graduate Studies in Mathematics) - Hardcover

Louis Halle Rowen

Hardcover

ISBN 10: 082184153X ISBN 13: 9780821841532

Publisher: American Mathematical Society,, 2008

Synopsis

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.

About this title

Review

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

Edition details

• Publisher: American Mathematical Society,
• Publication date: 2008
• Language: English
• ISBN 10: 082184153X
• ISBN 13: 9780821841532
• Binding: Hardcover
• Number of pages: 648