Noncommutative Algebra (Hardcover, 1993 ed.)

This book is an introduction to the theory of noncommutative algebra. The core of the book is suitable for a one-semester course for graduate students. The approach, which is more homological than ring-theoretic, clarifies the subject and its relation to other important areas of mathematics, including K-theory, homological algebra, and representation theory. The main part of the book begins with a brief review of background material; the first chapter covers the basics of semisimple modules and rings, including the Wedderburn structure theorem; chapter two discusses the Jacobson radical, giving several different views; chapter three develops the theory of central simple algebras, including proofs of the Skolem-Noether and Double Centralizer theorems, with two famous theorems of Wedderburn and Frobenius given as applications; and chapter four is an introduction to the Brauer group and its relation to cohomology. The remaining chapters introduce several special topics: the notion of primitive ring is developed along lines parallel to that of simple rings; the representation theory of finite groups is combined with the Wedderburn Structure Theorem to prove Burnside's Theorem; the global dimension of a ring is studied using Kaplansky's elementary point of view; and the Brauer group of a commutative ring is introduced. Problems throughout the book provide concrete examples, applications and amplifications of the text; a set of supplementary problems explores further topics and can serve as starting points for student projects.

General

Imprint:	Springer-Verlag New York
Country of origin:	United States
Series:	Graduate Texts in Mathematics, 144
Release date:	August 1993
First published:	1993
Authors:	Benson Farb • R. Keith Dennis
Dimensions:	235 x 155 x 20mm (L x W x T)
Format:	Hardcover
Pages:	226
Edition:	1993 ed.
ISBN-13:	978-0-387-94057-1
Categories:	Books > Science & Mathematics > Mathematics > Algebra > Groups & group theory
LSN:	0-387-94057-X
Barcode:	9780387940571

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