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Noncommutative Algebra (Hardcover, 1993 ed.) Loot Price: R2,472
Discovery Miles 24 720
Noncommutative Algebra (Hardcover, 1993 ed.): Benson Farb, R. Keith Dennis

Noncommutative Algebra (Hardcover, 1993 ed.)

Benson Farb, R. Keith Dennis

Series: Graduate Texts in Mathematics, 144

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Loot Price R2,472 Discovery Miles 24 720 | Repayment Terms: R232 pm x 12*

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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
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LSN: 0-387-94057-X
Barcode: 9780387940571

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