ENGLISH

An algebraic introduction to K-theory

By Bruce A. Magurn

Book information

Publisher
Cambridge University Press
Year
2002
ISBN
0521800781, 9780521800785, 9780521106580, 0521106583
Google Books ID
QBXvmgZVvawC
Open Library ID
OL24087625M
Language
english
Format
DJVU
Filesize
3 MB (3654354 bytes)
Series
Encyclopedia of Mathematics and its Applications
Edition
1st
Pages
690\690
Topic
Mathematics Algebra
Library
Kolxo3
DPI
200
Orientation
yes
Scanned
yes
Time added
2010-07-29 05:14:56

Description

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.

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