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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 finitelygenerated semi-regular ideal $I$. In this article, we show that the class ofsemi-regular $w$-flat modules is a covering class. Utilizing these notions, wegive some homological characterizations of $\WQ$-rings and $Q_0$-\PvMR s.

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