What does this research mean for the field?

Under certain conditions, a commutative ring R is S-Noetherian if and only if every S-FP-injective R-module is S-injective, and S-counterparts exist for Matlis, Stenström, and Cheatham-Stone's characterizations of coherent rings. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

The aim is to define and explore S-FP-injective modules and their connection to S-Noetherian rings.

April 27, 2026

S -FP-injective modules

Key Points

The aim is to define and explore S-FP-injective modules and their connection to S-Noetherian rings.
Introduces the concept of S-FP-injective modules in the context of commutative rings.
Investigates relationships between S-FP-injective and S-injective modules.
Establishes characterizations of coherent rings in terms of S-structures.
A ring R is S-Noetherian if and only if every S-FP-injective R-module is S-injective under specific conditions.
Provides S-counterparts of established characterizations in coherent rings by Matlis, Stenström, and Cheatham–Stone.

Abstract

Abstract 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.

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