On (m, n)-injectivity of modules

Let R be a ring. For two Fixed positive integers in and n, a right R-module M is called (m,n)-injective if every right R-homomorphism from an n-generated submodule of R-m to M extends to one from R-m 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.