Let R be a ring. For two fixed positive integers m and n, a right R-module M is called (m, n)-injective in case every right R-homomorphism from an n-generated submodule of Rm to M extends to one from Rm to M. R is said to be left (m, n)-coherent if each n-generated submodule of the left R-module Rm is finitely presented. In this paper,we give some new characterizations of (m, n)-injective modules. We also derive various equivalent conditions for a ring to be left (m, n)-coherent. Some known results on coherent rings are obtained as corollaries.