Abstract
Recall that a commutative ring [Formula: see text] is a locally integral domain if its localization [Formula: see text] is an integral domain for each prime ideal [Formula: see text] of [Formula: see text] Our aim in this paper is to extend the notion of locally integral domains to modules. Let [Formula: see text] be a commutative ring with a unity and [Formula: see text] a nonzero unital [Formula: see text]-module. [Formula: see text] is called a locally torsion-free module if the localization [Formula: see text] of [Formula: see text] is a torsion-free [Formula: see text]-module for each prime ideal [Formula: see text] of [Formula: see text] 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.
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