On S-injective modules

Let R be a commutative ring with an identity, and S a multiplicative subset of R. In this paper, we introduce the notion of S-injective modules as a weak version of injective modules. Among other results, we provide an S-version of the Baer's characterisation of injective modules. We also give an S-version of the Lambek's characterization of flat modules: an R-module M is S-flat if and only if its character, Homₙ (M, Q/Z), is an S-injective R-module. As applications, we establish, under certain conditions, counterparts of Cheatham and Stone's characterizations for S-Noetherian rings using the notion of character modules.