Equivalence and Duality for Module Categories with Tilting and Cotilting for Rings (Cambridge Tracts in Mathematics, Series Number 161)

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 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. Robert R. Colby, Kent R. Fuller. Includes Bibliographical References (p. 147-150) And Index. "This book provides a unified approach to many of the theories of equivalence and duality between categories of modules that have 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 functions, 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."--BOOK JACKET This book provides a unified and innovative approach to much of the theories of equivalence and duality between categories of modules that has transpired over the last 45 years. The authors discuss the 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 Providing a unified approach to much of the theories of equivalence and duality between categories of modules that has transpired over the last 45 years, the authors investigate relationships between categories of modules over a pair of rings that are induced by covariant and contravariant representable functors