Abstract
Given two ringsRandS, we study the category equivalences T⇄Y, where T is a torsion class ofR-modules and Y is a torsion-free class ofS-modules. These equivalences correspond to quasi-tilting triples (R,V,S), whereRVSis a bimodule which has, “locally,” a tilting behavior. Comparing this setting with tilting bimodules and, more generally, with the torsion theory counter equivalences introduced by Colby and Fuller, we prove a local version of the Tilting Theorem for quasi-tilting triples. A whole section is devoted to examples in case of algebras over a field.
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