Quasi-Tilting Modules and Counter Equivalences Original Research Article

Given two ringsRandS, we study the category equivalences image right arrow over left arrow image, where image is a torsion class ofR-modules and image 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.