Equivalence and Duality for Module Categories with Tilting and Cotilting for Rings
1st Edition
Published on 17. May 2006
978-0-511-18984-5 (ISBN)
Description
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.
Reviews / Votes
'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 MATHMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Publishing group
Cambridge University Press
Target group
Professional and scholarly
College/higher education
Illustrations
Worked examples or Exercises
File size
1,06 MB
ISBN-13
978-0-511-18984-5 (9780511189845)
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Schweitzer Classification
Other editions
Additional editions
Robert R. Colby | Kent R. Fuller
Equivalence and Duality for Module Categories with Tilting and Cotilting for Rings
Book
03/2004
Cambridge University Press
€147.50
Shipment within 15-20 days
Persons
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. Kent R. Fuller is a professor of mathematics at the University of Iowa. He is the author or coauthor of more than 70 research papers in ring and module theory, a dozen of which are joint work with Robert R. Colby. He is also coauthor of the widely known Rings and Categories of Modules. He has lectured on his research in several countries and is a member of the editorial board of the Journal of Algebra and belongs to the American Mathematical Society.
Content
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.
