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Graduate Algebra Noncommutative View 1st Edition by Louis Halle Rowen 082184153X 9780821841532

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Graduate Algebra Noncommutative View 1st Edition Louis Halle Rowen Digital Instant Download

Author(s): Louis Halle Rowen
ISBN(s): 9780821841532, 082184153X
Edition: 1
File Details: PDF, 8.48 MB
Year: 2008
Language: english
SKU: EB-4629474 Category: Tag:

Graduate Algebra Noncommutative View 1st Edition by Louis Halle Rowen – Ebook PDF Instant Download/Delivery: 082184153X, 9780821841532

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Product details:

ISBN 10: 082184153X 

ISBN 13: 9780821841532

Author: 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:

Part IV: The Structure of Rings

  1. Fundamental Concepts in Ring Theory

  2. Semisimple Modules and Rings and the Wedderburn-Artin Theorem

  3. The Jacobson Program Applied to Left Artinian Rings

  4. Noetherian Rings and the Role of Prime Rings

  5. Algebras in Terms of Generators and Relations

  6. Tensor Products

  7. Exercises – Part IV

Part V: Representations of Groups and Lie Algebras

  1. Group Representations and Group Algebras

  2. Characters of Finite Groups

  3. Lie Algebras and Other Nonassociative Algebras

  4. Dynkin Diagrams (Coxeter-Dynkin Graphs and Coxeter Groups)

  5. Exercises – Part V

Part VI: Representable Algebras

  1. Polynomial Identities and Representable Algebras

  2. Central Simple Algebras and the Brauer Group

  3. Homological Algebra and Categories of Modules

  4. Hopf Algebras

  5. Exercises – Part VI

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