An Algebraic Introduction to K-Theory (Hardcover)

Bruce A. Magurn

ISBN 10: 0521800781 / ISBN 13: 9780521800785

Published by Cambridge University Press, Cambridge, 2002

About this Item

Hardcover. 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 organizes 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, localization, Jacobson radical, chain conditions, Dedekind domains, semisimple 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. 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. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability.

Seller Inventory # 9780521800785

Bibliographic Details

• Title: An Algebraic Introduction to K-Theory (Hardcover)
• Publisher: Cambridge University Press, Cambridge
• Publication Date: 2002
• Language: English
• ISBN 10: 0521800781
• ISBN 13: 9780521800785
• Binding: Hardcover
• Condition: new

About this title

Synopsis

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

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

Review of the hardback: 'This is a fine introduction to algebraic K-theory, requiring only a basic preliminary knowledge of groups, rings and modules.' European Mathematical Society

Review of the hardback: '... a fine introduction to algebraic K-theory ...' EMS Newsletter

Review of the hardback: '... an excellent introduction to the algebraic K-theory.' Proceedings of the Edinburgh Mathematical Society