On A Generalization of Small-Injective Modules - Zone, Zahraa Abbas; Mehdi, Akeel Ramadan (Iraqi Journal of Science, 2024)
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.