On NN-torsion-free and NN-injective modules

Abstract

In this paper, we introduce the concept of NN-torsion-free modules (respectively, NN-injective modules) as a generalization of nonnil-torsion-free modules (respectively, injective modules). We show that they behave in a way similar to the classical ones. As an application, we characterize ϕ-rings over which every NN-torsion-free module is NN-injective.