Some Generalizations of Small Injective Modules

Let R be a ring. Let m and n be positive integers, a right R-module M is called (m,n)-small injective, if every right R-homomorphism from an n-generated submodule of J^m to M extends to one from R^m to M. A ring R is called right (m,n)-small injective if the right R module RR is (m,n)-small injective. In this paper, we give some properties of (m,n)-small injective modules and right (m,n)-small injective rings.