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.

KEYWORDS:

• NN-injective module
• NN-torsion-free module
• nonnil-commutative diagram

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 13C11
• 13C12
• 13C60

Additional information

Funding

This work was financially supported by the National Natural Science Foundation of China 12061001, the Sichuan Science and Technology Program 2023ZYD0005, 2023NSFSC0074, and Aba Teachers University 20210103002, 20212001128.