Robert R. Colby

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

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 22. März 2004
• Englisch
• ISBN-13: 9780511189845
• Artikelnr.: 38215692

Autorenporträt

Robert R. Colby is Professor Emeritus at the University of Hawaii and Independent Scholar at the University of Iowa. He is also a member emeritu of the American Mathematical Society. He is responsible for the definition of generalized Morita duality and was one of the first to consider the tilting and cotilting theory of finite dimensional algebras in the more general setting of general ring theory.

Inhaltsangabe

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.