On qdf modules and qdf rings

Abstract

The purpose of this paper is to further the study of weakly injective and weakly tight modules a generalization of injective modules. A right R-module M is said to be weakly tight (tight) if every finitely generated submodule N of its injective hull E (M) is embeddable in a direct sum of copies of M (is embeddable in M). For some classes K of modules, we study when direct sums of modules from K are weakly tight, tight, weakly injective. In particular, we get necessary and sufficient conditions for sum-weak tightness of the injective hull of a