A homological characterization of $Q_0$-Pr\"{u}fer $v$-multiplication rings

TL;DR

This paper introduces a homological approach to characterize $Q_0$-Prüfer $v$-multiplication rings using semi-regular $w$-flat modules and explores their properties within the framework of commutative algebra.

Contribution

It provides the first homological characterization of $Q_0$-Prüfer $v$-multiplication rings via semi-regular $w$-flat modules and establishes their role as a covering class.

Findings

Semi-regular $w$-flat modules form a covering class.

Homological criteria for $ ext{WQ}$-rings are established.

Characterizations of $Q_0$-Prüfer $v$-multiplication rings are provided.

Abstract

Let $R$ be a commutative ring. An $R$-module $M$ is called a semi-regular $w$-flat module if $\Tor_1^R(R/I,M)$ is $\GV$-torsion for any finitely generated semi-regular ideal $I$. In this article, we show that the class of semi-regular $w$-flat modules is a covering class. Utilizing these notions, we give some homological characterizations of $\WQ$-rings and $Q_0$-\PvMR s.