num_pages: 692
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.
language: English
title: An Algebraic Introduction to K-Theory
publisher: Cambridge University Press