Graduate algebra : noncommutative view / Louis Halle Rowen.

Format:

Book

Author/Creator:

Rowen, Louis Halle, author.

Series:

Graduate studies in mathematics ; v. 91.

Graduate studies in mathematics ; volume 91

Language:

English

Subjects (All):

Commutative algebra.

Geometry, Algebraic.

Geometry, Affine.

Commutative rings.

Modules (Algebra).

Physical Description:

1 online resource (679 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2008]

Language Note:

English

Summary:

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.

Contents:

""Cover""; ""Title page""; ""Contents""; ""Introduction""; ""List of symbols""; ""Prerequisites""; ""Part IV. The structure of rings""; ""Introduction to the structure of rings""; ""Fundamental concepts in ring theory""; ""Semisimple modules and rings and the Wedderburn-Artin theorem""; ""The Jacobson program applied to left Artinian rings""; ""Noetherian rings and the role of prime rings""; ""Algebras in terms of generators and relations""; ""Tensor products""; ""Exercises�Part IV""; ""Part V. Representations of groups and Lie algebras""

""Introduction to representations of groups and Lie algebras""""Group representations and group algebras""; ""Characters of finite groups""; ""Lie algebras and other nonassociative algebras""; ""Dynkin diagrams (Coxeter-Dynkin graphs and Coxeter groups)""; ""Exercises�Part V""; ""Part VI. Representable algebras""; ""Introduction to representable algebras""; ""Polynomial identities and representable algebras""; ""Central simple algebras and the Brauer group""; ""Homological algebra and categories of modules""; ""Hopf algebras""; ""Exercises�Part VI""; ""List of major results""

""Bibliography""""List of names""; ""Index""; ""Back Cover""

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (ebrary, viewed April 11, 2015).

Description based on publisher supplied metadata and other sources.

ISBN:

9781470418021

1470418029

OCLC:

922965180