Noncommutative Algebra: NONCOMMUTATIVE ALGEBRA

Hardcover | August 20, 1993

byBenson Farb, R. Keith Dennis

not yet rated|write a review
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.

Pricing and Purchase Info

$110.50

In stock online
Ships free on orders over $25

From the Publisher

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...

Format:HardcoverDimensions:240 pages, 9.25 × 6.1 × 0.27 inPublished:August 20, 1993Publisher:Springer New York

The following ISBNs are associated with this title:

ISBN - 10:038794057X

ISBN - 13:9780387940571

Look for similar items by category:

Customer Reviews of Noncommutative Algebra: NONCOMMUTATIVE ALGEBRA

Reviews