QUASI-TILTING MODULES AND COUNTER EQUIVALENCES

Given two rings R and S, we study the category equivalences T reversib le arrow Y, where T is a torsion class of R-modules and Y is a torsion -free class of S-modules. These equivalences correspond to quasi-tilti ng triples (R, V, S), where V-R(S) is a bimodule which has, ''locally, '' a tilting behavior. Comparing this setting with tilting bimodules a nd, more generally, with the torsion theory counter equivalences intro duced by Colby and Fuller, we prove a local version of the Tilting The orem for quasi-tilting triples. A whole section is devoted to examples in case of algebras over a field. (C) 1997 Academic Press.