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

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

A. J. Berrick (Author), M. E. Keating (Author)

9780521632744, Cambridge University Press

Hardback, published 1 May 2000

284 pages, 175 exercises
22.9 x 15.2 x 1.9 cm, 0.59 kg

'… an excellent concise introduction to the theory of rings and modules …'. Tong Wenting, Zentralblatt MATH

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. 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' companion volume Categories and Modules, soon to appear. Armed with these two texts, the reader will be ready for more advanced topics in K-theory, homological algebra and algebraic number theory.

1. Basics
2. Direct sums and their short exact sequences
3. Noetherian rings and polynomial rings
4. Artinian rings and modules
5. Dedekind domains
6. Modules over Dedekind domains.

Subject Areas: Algebra [PBF]