Locally torsion-free modules - TEKİR, ÜNSAL; KOÇ, SUAT (My University, 2022)
© 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.
Keywords: 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