Semi-regular flat modules over strong Prüfer rings

Abstract

We first introduce and study the notion of semi-regular flat modules, and then show that a ring R is a strong Prüfer 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.