S-FP-injective modules

TL;DR

This paper introduces the concept of S-FP-injective modules over commutative rings and explores their properties, including characterizations of S-Noetherian and S-coherent rings, extending classical module theory results.

Contribution

It defines S-FP-injective modules and establishes new characterizations of S-Noetherian and S-coherent rings related to these modules.

Findings

S-Noetherian rings characterized by S-FP-injective modules

Counterparts of classical ring characterizations for S-coherent rings

Conditions under which S-FP-injective modules are S-injective

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.