Noncommutative Rings

by Herstein, I. N.

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Title Statements

Full title :Noncommutative Rings / I.N. Herstein.

Summary

This beautiful book is the result of the author's wide and deep knowledge of the subject matter, combined with a gift for exposition ... The well selected material is offered in an integrated presentation of the structure theory of noncommutative (associative rings) and its applications. The book will appeal to many a reader. It would be wonderful as a textbook, and in fact, it's based on the author's lecture notes ... Only people looking for the most general form of a particular theorem are advised to turn to other books, but those interested in studying or reviewing its subject matter or looking for a rounded account of it, could do no better than choosing this book for this purpose. Bulletin of the American Mathematical Society Noncommutative Rings provides a cross-section of ideas, techniques and results that give the reader an idea of that part of algebra which concerns itself with noncommutative rings. In the space of 200 pages, Herstein covers the Jacobson radical, semisimple rings, commutativity theorems, simple algebras, representations of finite groups, polynomial identities, Goldie's theorem and the Golod-Shafarevitch theorem. Almost every practicing ring theorist has studied portions of this classic monograph.

Edition Statements

Publication Date:©1994

Publication Statements

Publisher(s):Mathematical Association of America
Place of Publication:Washington, District of Columbia
Language:eng
Publication Date:©1994

The Physical Object

Description:1 online resource (215 pages) : : illustrations.

Edition Identifiers

ISBN:9781614440154, 1614440158, 0883850397, 9780883850398, 088385015X, 9780883850152
oclc:ocn880452865
LC Classification:QA251.4
Dewey Decimal:512/.815

""Front Cover""; ""Noncommutative Rings""; ""Copyright Page""; ""Contents""; ""Chapter 1. The Jacobson Radical""; ""1. Modules""; ""2. The radical of a ring""; ""3. Artinian rings""; ""4. Semisimple Artinian rings""; ""References""; ""Chapter 2. Semisimple Rings""; ""1. The density theorem""; ""2. Semisimple rings""; ""3. Applications of Wedderburn's theorem""; ""References""; ""Chapter 3. Commutativity Theorems""; ""1. Wedderburn's Theorem and some generalizations""; ""2. Some special rings""; ""References""; ""Chapter 4. Simple Algebras""; ""1. The Brauer group""; ""2. Maximal subfields""

""3. Some classic theorems""""4. Crossed products""; ""References""; ""Chapter 5. Representations of Finite Groups""; ""1. The elements of the theory""; ""2. A theorem of Hurwitz""; ""3. Applications to group theory""; ""References""; ""Chapter 6. Polynomial Identities""; ""1. A result on radicals""; ""2. Standard identities""; ""3. A theorem of Kaplansky""; ""4. The Kurosh Problem for P.I. algebras""; ""References""; ""Chapter 7. Goldie's Theorem""; ""1. Ore's theorem""; ""2. Goldie's theorems""; ""3. Ultra-products and a theorem of Posner""; ""References""

""Chapter 8. The Golod-Shafarevitc…