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

This book provides a unified approach to much of the theories of equivalence and duality between categories of modules.

Robert R. Colby (Author), Kent R. Fuller (Author)

9780521838214, Cambridge University Press

Hardback, published 22 March 2004

162 pages
23.4 x 16 x 1.7 cm, 0.385 kg

'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

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. In particular, during the past dozen or so years 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. By here collecting and unifying the basic results of these investigations with innovative and easily understandable proofs, the authors' aim is to provide an aid to further research in this central topic in abstract algebra, and a reference for all whose research lies in this field.

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.

Subject Areas: Algebra [PBF]