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 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.

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

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.