Noncommutative RingsCambridge University Press, 8 sept. 2005 - 202 pages 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. |
Table des matières
THE JACOBSON RADICAL | 1 |
SEMISIMPLE RINGS | 39 |
COMMUTATIVITY THEOREMS | 69 |
SIMPLE ALGEBRAS | 89 |
REPRESENTATIONS OF FINITE GROUPS | 124 |
POLYNOMIAL IDENTITIES | 150 |
GOLDIES THEOREM | 169 |
THE GOLODSHAFAREVITCH THEOREM | 187 |
Expressions et termes fréquents
addition algebra over F annihilator assume basis central simple character characteristic claim Clearly closed commutative commuting ring complex conclude conjugate consequence consider contains COROLLARY define DEFINITION dimensional direct sum division algebra division ring equivalent essential established exists fact factor set field finite group finite-dimensional follows forces function give given hence homomorphic idempotent independent induction infinite integer irreducible irreducible representation isomorphic leave left ideal Lemma linearly locally finite mapping Math matrices maximal maximal subfield merely minimal module Moreover nature nilpotent nonzero normal Note particular polynomial identity prime primitive ring problem Proof prove radical reader regular relation representation representation of G result right ideal roots satisfies semisimple shown simple algebra structure subgroup Suppose theorem theory tion unit element vector space write yields