S-injective modules.

Let S be a multiplicative subset of a ring R with unity. A unitary right R-module M is referred to as S-injective if there exist an element s ∈ S and an injective R-submodule Q of M such that M s ⊆ Q ⊆ M . In this paper, we study the structure of S-injective modules which extend the notion of injective modules. Some characterizations and various examples of S-injective modules are provided, and the S-variants of Baer’s criterion, the Bass-Papp theorem, and the Eakin-Nagata-Eisenbud theorem are proven. [ABSTRACT FROM AUTHOR]