An Algebraic Introduction to K-Theory
Series: Encyclopedia of Mathematics and its Applications; 87;
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Estimated delivery time: In stock at the publisher, but not at Prospero's office. Delivery time approx. 3-5 weeks.
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Product details:
- Publisher Cambridge University Press
- Date of Publication 20 May 2002
- ISBN 9780521800785
- Binding Hardback
- No. of pages692 pages
- Size 242x162x39 mm
- Weight 1106 g
- Language English 0
Categories
Short description:
An introduction to algebraic K-theory with no prerequisite beyond a first semester of algebra.
MoreLong description:
This is an introduction to algebraic K-theory with no prerequisite beyond a first semester of algebra (including Galois theory and modules over a principal ideal domain). The presentation is almost entirely self-contained, and is divided into short sections with exercises to reinforce the ideas and suggest further lines of inquiry. No experience with analysis, geometry, number theory or topology is assumed. Within the context of linear algebra, K-theory organises and clarifies the relations among ideal class groups, group representations, quadratic forms, dimensions of a ring, determinants, quadratic reciprocity and Brauer groups of fields. By including introductions to standard algebra topics (tensor products, localisation, Jacobson radical, chain conditions, Dedekind domains, semi-simple rings, exterior algebras), the author makes algebraic K-theory accessible to first-year graduate students and other mathematically sophisticated readers. Even if your algebra is rusty, you can read this book; the necessary background is here, with proofs.
Review of the hardback: '... this is a well written introduction to the theory of the algebraic K-groups Ko, K1 and K2; the author has done a wonderful job in presenting the material in a clear way that will be accessible to readers with a modest background in algebra.' Franz Lemmermeyer, Zentralblatt MATH
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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