On A Generalization of Small-Injective Modules

Let R be a ring. JS-injective right R-modules are introduced and studied in this paper as a generalization of small-injective right R-modules. Let N and M be right R-modules. A module M is said to be JS-N-injective if every R-homomorphism from a submodule of J(N) J(R) into M extends to N. If a module M is JS-R-injective, then M is called JS-injective. Many characterizations and properties of JS-injective right R-modules are obtained. Rings over which every right module is JS-injective are characterized. We study quotients of JS-injective right modules. Then we give conditions under which the class of JS-injective right modules is closed under direct sums.