Almost complete tilting modules

Abstract

Let A A be a finite-dimensional hereditary algebra over an algebraically closed field. All modules will be finite-dimensional left A A -modules. We are concerned with partial tilting modules which can be completed to a tilting module by one indecomposable module which will be called a complement. As a main result we show that such a partial tilting module allows (up to isomorphism) at most two complements and there are two such complements if and only if the partial tilting module is sincere.