S -FP-injective modules

Let R be a commutative ring and S 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, S -counterparts of Matlis, Stenström and Cheatham–Stone’s characterizations of coherent rings.