On (m, n)-injectivity of modules

Abstract

Let R be a ring. For two fixed positive integers m and n, a right R-module M is called (m, n)-injective if every right R-homomorphism from an n-generated submodule of Rm to M extends to one from Rm to M. This definition unifies several definitions on generalizations of injectivity of modules. The aim of this paper is to investigate properties of the (m, n)-injective modules. Various results are developed, many extending known results.