S-FP-injective modules

Abstract

Let R be a commutative ring, and let S be a multiplicative subset of R. In this paper, we introduce and investigate the notion of S-FP-injective modules. Among other results, we show that, under certain conditions, a ring R is S-Noetherian if and only if every S-FP-injective R-module is S-injective. Moreover, we establish, under certain conditions, counterparts of Matlis, Stenstr\"om and Cheatham-Stone's characterizations of S-coherent rings.