COTILTING CLASSES OF TORSION-FREE MODULES

A right R-module M is torsion-free (in the sense of Hattori) if [Formula: see text] for all r ∈ R. The class of torsion-free modules is a cotilting class if and only if R is a left p.p.-ring. This paper investigates how the class of torsion-free modules is related to the cotilting classes arising from embeddings of a right (left) non-singular ring R into its maximal right (left) ring of quotients. Several applications are given.