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This book is both an introduction to K-theory and a text in algebra. These two roles are entirely compatible. On the one hand, nothing more than the basic algebra of groups, rings, and modules is needed to explain the clasical algebraic K-theory. On the other hand, K-theory is a natural organizing principle for the standard topics of a second course in algebra, and these topics are presented carefully here. The reader will not only learn algebraic K-theory, but also Dedekind domains, class groups, semisimple rings, character theory, quadratic forms, tensor products, localization, completion, tensor algebras, symmetric algebras, exterior algebras, central simple algebras, and Brauer groups. The presentation is self-contained, with all the necessary background and proofs, and is divided into short sections with exercises to reinforce the ideas and suggest further lines of inquiry. The prerequisites are minimal: just a first semester of algebra (including Galois theory and modules over a principal ideal domain). No experience with homological algebra, analysis, geometry, number theory, or topology is assumed. The author has successfuly used this text to teach algebra to first year graduate students. Selected topics can be used to construct a variety of one-semester courses; coverage of the entire text requires a full year.Read more
- A self-contained exposition of the main theorems of classical algebraic K-theory
- Accessible to anyone with a good first semester introduction to algebra
- The methods are entirely algebraic, unlike other treatments which require some advanced knowledge of topology, geometry, or functional analysis
Reviews & endorsements
"This volume is a very useful graduate algebra text with an orientation towards algebraic K-theory....This volume will form an excellent basis for several types of one-and two-semester graduate algebra courses." Mathematical Reviews
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- Date Published: February 2010
- format: Paperback
- isbn: 9780521106580
- length: 692 pages
- dimensions: 234 x 156 x 35 mm
- weight: 0.95kg
- availability: Available
Table of Contents
1. Groups of modules: Ko
2. Sources of Ko
3. Groups of matrices: K1
4. Relations among matrices: K2
5. Sources of K2.
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