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

ISBN-13: 9780521632744 / Angielski / Twarda / 2000 / 284 str.

A. J. Berrick; M. E. Keating; B. Bollobas

Opis

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.

Recenzje

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

Spis treści

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.