An Introduction to Rings and Modules: With K-Theory in View

Front Cover
Cambridge University Press, 2000 - Mathematics - 265 pages
This concise introduction to ring theory, module theory and number theory is ideal for a first year graduate student, as well as being an excellent reference for working mathematicians in other areas. Starting from definitions, the book introduces fundamental constructions of rings and modules, as direct sums or products, and by exact sequences. It then explores the structure of modules over various types of ring: noncommutative polynomial rings, Artinian rings (both semisimple and not), and Dedekind domains. It also shows how Dedekind domains arise in number theory, and explicitly calculates some rings of integers and their class groups. About 200 exercises complement the text and introduce further topics. This book provides the background material for the authors' forthcoming companion volume Categories and Modules. Armed with these two texts, the reader will be ready for more advanced topics in K-theory, homological algebra and algebraic number theory.
 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

Exercises
11
DIRECT SUMS AND SHORT EXACT SEQUENCES
36
NOETHERIAN RINGS AND POLYNOMIAL RINGS
108
ARTINIAN RINGS AND MODULES
145
DEDEKIND DOMAINS
186
MODULES OVER DEDEKIND DOMAINS
224
References
252
Copyright

Other editions - View all

Common terms and phrases

Bibliographic information