Equivalence and Duality for Module Categories (with Tilting and Cotilting for Rings)

ISBN-13: 9780521838214 / Angielski / Twarda / 2004 / 152 str.

R. R. Colby; K. R. Fuller; Robert R. Colby

Opis

This book provides a unified approach to much of the theories of equivalence and duality between categories of modules that has transpired over the last 45 years. More recently, many authors (including the authors of this book) have investigated relationships between categories of modules over a pair of rings that are induced by both covariant and contravariant representable functors, in particular, by tilting and cotilting theories. Collecting and unifying the basic results of these investigations with innovative and easily understandable proofs, the authors provide an aid to further research on this central topic in abstract algebra.

Recenzje

'This book of the well-known specialists represents a valuable study of a topical algebraic problem, it contains many important results, which can stimulate the subsequent development of this domain. With clear and accessible account, with all necessary proofs and various examples, this work is very useful both for study and research.' Zentralblatt MATH

Spis treści

0. Preface; 1. Some module theoretic observations; 2. Representable equivalences; 3. Tilting modules; 4. Representable dualities; 5. Cotilting; A. Adjoints and category equivalence; B. Noetherian serial rings.