Some new module-theoretic characterizations of $S$-coherent rings

TL;DR

This paper introduces new module-theoretic concepts like s-pure exact sequences and s-absolutely pure modules, providing novel characterizations of S-coherent rings in commutative algebra.

Contribution

It extends classical notions to define s-pure and s-absolutely pure modules, offering fresh characterizations of S-coherent rings.

Findings

Defined s-pure exact sequences and s-absolutely pure modules.

Provided new characterizations of S-coherent rings.

Extended classical pure module concepts to the S-coherent context.

Abstract

Let $R$ be a commutative ring with identity and $S$ a multiplicative subset of $R$. In this paper, we first introduce and study the notions of $s$-pure exact sequences and $s$-absolutely pure modules which extend the classical notions of pure exact sequences and absolutely pure modules. And then, we give some new characterizations of $S$-coherent rings in terms of $s$-absolutely pure modules.