Categories and Modules with K-Theory in View: 67 (Cambridge Studies in Advanced Mathematics, Series Number 67) - Hardcover

Berrick, A. J.; Keating, M. E.

Hardcover

ISBN 10: 0521632765 ISBN 13: 9780521632768

Publisher: Cambridge University Press, 2000

Synopsis

This book, first published in 2000, is a concise introduction at graduate level to ring theory, module theory and number theory.

About this title

Book Description

This book, first published in 2000, is a concise introduction to ring theory, module theory and number theory, ideal for a first year graduate student, as well as an excellent reference for working mathematicians in other areas. About 200 exercises complement the text and introduce further topics.

Synopsis

This book develops aspects of category theory fundamental to the study of algebraic K-theory. Ring and module theory illustrates category theory which provides insight into more advanced topics in module theory. Starting with categories in general, the text then examines categories of K-theory. This leads to the study of tensor products and the Morita theory. The categorical approach to localizations and completions of modules is formulated in terms of direct and inverse limits, prompting a discussion of localization of categories in general. Finally, local-global techniques which supply information about modules from their localizations and completions and underlie some interesting applications of K-theory to number theory and geometry are considered. Many useful exercises, concrete illustrations of abstract concepts placed in their historical settings and an extensive list of references are included. This book will help all who wish to work in K-theory to master its prerequisites.

Edition details

• Publisher: Cambridge University Press
• Publication date: 2000
• Language: English
• ISBN 10: 0521632765
• ISBN 13: 9780521632768
• Binding: Hardcover
• Number of pages: 380