Semi-regular flat modules over strong Pr\"{u}fer rings.

We first introduce and study the notion of semi-regular flat modules, and then show that a ring $R$ is a strong \Prufer\ ring if and only if every submodule of a semi-regular flat $R$-module is semi-regular flat, if and only if every ideal of $R$ is semi-regular flat, if and only if every $R$-module has a surjective semi-regular flat (pre)envelope.