Categories and Modules with K-Theory in View

Erscheinungsjahr 2012
ISBN: 978-0-521-63276-8
Verlag: Cambridge University Press

Buch, Englisch, Band 67, 380 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 766 g

Reihe: Cambridge Studies in Advanced Mathematics

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.

Autoren/Hrsg.

Berrick, A. J.

Keating, M. E.

Bollobas, Bela

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Homologische Algebra

Inhaltsverzeichnis

1. Categories; 2. Categories and exact sequences; 3. Change of rings; 4. The Morita theory; 5. Limits in categories; 6. Localisation; 7. Local-global methods.