TILTING MODULES AND THE SUBCATEGORIES C

In this paper we further study the full subcategories CM i of the category of finitely generated modules over an artin algebra introduced in [PP], consisting of the modules having an addM resolution of length i, which remains exact under the functor HomA(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.