Abstract
In this case, the left module BT becomes again a generalized tilting module with End(,T) = A [8]. It should be noted here that the notion of generalized tilting modules is fairly general and the class of such modules contains all tilting modules of finite projective dimension in the sense of Miyashita [6] and also all cotilting modules of finite injective dimension. Especially, the injective cogenerator DA is always a generalized tilting module even if the regular module A has infinite injective dimension on each side. In the joint work with Tachikawa [7], we proved the existence of a stably equivalent functor &-T(A) %&-T(B) for any genuine tilting module defined by Happel and Ringle [S] by introducing torsion and torsion-free resolutions of modules. We have tried to generalize the existence
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