On gs-pseudo-injective modules

As a proper generalization of pseudo-injectivity, we introduce and investigate gs-pseudo-injective modules. A right module M over a ring R is said to be gs-pseudo-N-injective (where N is a right R-module) if every R-monomorphism from a submodule of soc (N) soc (RR) into M extends to N. A module M is said to be gs-pseudo-injective, if M is gs-pseudo-M-injective. We obtain various characterizations and properties of these modules. Some results on pseudo-injectivity are extended to gs-pseudo-injectivity.