Locally torsion-free modules

Recall that a commutative ring R is a locally integral domain if its localization Rp is an integral domain for each prime ideal P of R. Our aim in this paper is to extend the notion of locally integral domains to modules. Let R be a commutative ring with a unity and M a nonzero unital R-module. M is called a locally torsion-free module if the localization M p of M is a torsion-free Rp-module for each prime ideal P of R. In addition to giving many properties of locally torsion-free modules, we use them to characterize Baer modules, torsion free modules, and von Neumann regular rings.