Publication: Locally torsion-free modules
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Date
2022-01-01
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Abstract
© 2023 World Scientific Publishing Company.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 MP 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.
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Matematik, Bilgisayar Bilimleri, Temel Bilimler, Mathematics, Computer Science, Natural Sciences, Temel Bilimler (SCI), MATEMATİK, UYGULAMALI, Natural Sciences (SCI), MATHEMATICS, MATHEMATICS, APPLIED, Algebra and Number Theory, Physical Sciences, Applied Mathematics, Baer modules, Baer rings, locally integral domains, locally torsion-free modules, normal modules, quasi-regular modules, quasi-regular rings, torsion-free modules, von Neumann regular modules, von Neumann regular rings
Citation
Jayaram C., Uǧurlu E. A., TEKİR Ü., KOÇ S., "Locally torsion-free modules", Journal of Algebra and its Applications, 2022