Tilting modules and the subcategories CiM

Abstract

In this article we further study the full subcategories Ci M of the category of finitely generated modules over an Artin algebra introduced in Platzeck and Pratti (2000), consisting of the modules having an addM resolution of length i, which remains exact under the functor Hom A(M, -). In particular, we characterize tilting modules in terms of these categories and determine when the transpose of a tilting module is a tilting module.