Download or read book Equivalence and Duality for Module Categories with Tilting and Cotilting for Rings written by Robert R. Colby and published by Cambridge University Press. This book was released on 2004-03-22 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.