Categories and Modules ith K-Theory in Vie [Hardcover]

This book, first published in 2000, is a concise introduction at graduate level to ring theory, module theory and number theory.This book develops aspects of category theory fundamental to the study of algebraic K-theory. Ring and module theory illustrates category theory which, in turn, provides insight into more advanced topics in module theory. 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.This book develops aspects of category theory fundamental to the study of algebraic K-theory. Ring and module theory illustrates category theory which, in turn, provides insight into more advanced topics in module theory. 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.This book develops aspects of category theory fundamental to the study of algebraic K-theory. Starting with categories in general, the text then examines categories of K-theory and moves on to tensor products and the Morita theory. The categorical approach to localizations and completions of modules is formulated in terms of direct and inverse limits. The authors consider local-global techniques that supply information about modules from their localizations and completions and underlie some interesting applications of K-theory to number theory and geometry. Many useful exercises, concrete illustrations of abstract concepts, and an extensive list of references are included.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.