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

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.