The object of this paper is to study the relationship between certain projective modules and their endomorphism rings. Specifically, the basic problem is to describe the projective modules whose endomorphism rings are (von Neumann) regular, local semiperfect, or left perfect. Call a projective module regular if every cyclic submodule is a direct summand. Thus a ring is a regular module if it is...

We prove that any infinitely generated tilting module is of finite type, namely that its associated tilting class is the Ext-orthogonal of a set of modules possessing a projective resolution consisting of finitely generated projective modules.