On uniformly $S$-coherent rings

TL;DR

This paper introduces and investigates uniformly $S$-coherent rings and modules, extending existing concepts with a uniform approach, and establishes several classical theorems in this new context.

Contribution

It defines uniformly $S$-finitely presented modules and rings, and proves uniform versions of Chase's, Chase's, and Matlis's theorems.

Findings

Established uniform versions of classical theorems

Introduced new notions of uniformly $S$-finitely presented modules

Extended the theory of $S$-coherent rings with uniform properties

Abstract

In this paper, we introduce and study the notions of uniformly $S$-finitely presented modules and uniformly $S$-coherent rings (modules) which are "uniform" versions of ($c$-)$S$-finitely presented modules and ($c$-)$S$-coherent rings (modules) introduced by Bennis and Hajoui \cite{bh18}. Among the results, uniformly $S$-versions of Chase's result, Chase Theorem and Matlis Theorem are obtained.