Rings and Categories of Modules

Graduate Texts in Mathematics #13

by F.W. Anderson, K.R. Fuller

This book is intended to provide a self-contained account of much of the theory of rings and modules. The theme of the text throughout is the relationship between the one-sided ideal structure a ring may possess and the behavior of its categories of modules. Following a brief outline of the foundations, the book begins with the basic definitions and properties of rings, modules and homomorphisms. The remainder of the text gives comprehensive treatments of direct sums, finiteness conditions, the Wedderburn-Artin Theorem, the Jacobson radical, the hom and tensor functions, Morita equivalence and duality, decomposition theory, and semiperfect and perfect rings. This second edition includes a chapter containing many of the classical results on Artinian rings that have helped form the foundation for much of contemporary research on the representation theory of Artinian rings and finite-dimensional algebras.

Genres: Mathematics

339 pages, Paperback

First published August 2, 1974

Reviews

[Ojas · Rating 4 out of 5]

great book on rings and modules, referenced in plenty of papers on algebra and functional analysis, nice problems and text is fairly readable, has lots of nice material