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Equivalence and Duality for Module Categories with Tilting and Cotilting for Rings (Cambridge Tracts in Mathematics)

Equivalence and Duality for Module Categories with Tilting and Cotilting for Rings (Cambridge Tracts in Mathematics)

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Robert R. Colby, Kent R. Fuller
Cambridge University Press, 3/22/2004
EAN 9780521838214, ISBN10: 0521838215

Hardcover, 162 pages, 23.4 x 16 x 1.7 cm
Language: English

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.