Introductory Lectures on Rings and Modules

A first-year graduate text or reference for advanced undergraduates on noncommutative aspects of rings and modules.

John A. Beachy (Author)

9780521643405, Cambridge University Press

Hardback, published 22 April 1999

248 pages, 250 exercises
23.6 x 15.7 x 1.9 cm, 0.465 kg

'… an excellent introduction …' European Mathematical Society

The focus of this book is the study of the noncommutative aspects of rings and modules, and the style will make it accessible to anyone with a background in basic abstract algebra. Features of interest include an early introduction of projective and injective modules; a module theoretic approach to the Jacobson radical and the Artin-Wedderburn theorem; the use of Baer's criterion for injectivity to prove the structure theorem for finitely generated modules over a principal ideal domain; and applications of the general theory to the representation theory of finite groups. Optional material includes a section on modules over the Weyl algebras and a section on Goldie's theorem. When compared to other more encyclopedic texts, the sharp focus of this book accommodates students meeting this material for the first time. It can be used as a first-year graduate text or as a reference for advanced undergraduates.

Preface
1. Rings
2. Modules
3. Structure of noncommutative rings
4. Representations of finite groups
Appendix
Bibliography
List of symbols
Index.

Subject Areas: Algebra [PBF]