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An Introduction to Rings and Modules : With K-Theory in View - A. Jon Berrick

An Introduction to Rings and Modules

With K-Theory in View

Hardcover Published: 27th May 2011
ISBN: 9780521632744
Number Of Pages: 284

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This is a concise introduction to ring theory, module theory and number theory, ideal for a first year graduate student, as well as an excellent reference for working mathematicians in other areas. Starting from definitions, the book introduces fundamental constructions of rings and modules, as direct sums or products, and by exact sequences. It then explores the structure of modules over various types of ring: noncommutative polynomial rings, Artinian rings (both semisimple and not), and Dedekind domains. It also shows how Dedekind domains arise in number theory, and explicitly calculates some rings of integers and their class groups. About 200 exercises complement the text and introduce further topics. This book provides the background material for the authors' companion volume Categories and Modules, soon to appear. Armed with these two texts, the reader will be ready for more advanced topics in K-theory, homological algebra and algebraic number theory.

'... an excellent concise introduction to the theory of rings and modules ...'. Tong Wenting, Zentralblatt MATH

Basics
Direct sums and their short exact sequences
Noetherian rings and polynomial rings
Artinian rings and modules
Dedekind domains
Modules over Dedekind domains
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521632744
ISBN-10: 0521632749
Series: Cambridge Studies in Advanced Mathematics (Hardcover)
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 284
Published: 27th May 2011
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 22.86 x 15.24  x 1.91
Weight (kg): 0.59

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