Atıf İçin Kopyala
Jayaram C., Uǧurlu E. A., TEKİR Ü., KOÇ S.
Journal of Algebra and its Applications, cilt.22, sa.5, 2023 (SCI-Expanded)
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Yayın Türü:
Makale / Tam Makale
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Cilt numarası:
22
Sayı:
5
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Basım Tarihi:
2023
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Doi Numarası:
10.1142/s0219498823501037
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Dergi Adı:
Journal of Algebra and its Applications
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Derginin Tarandığı İndeksler:
Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
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Anahtar Kelimeler:
von Neumann regular rings, Baer rings, quasi-regular rings, locally integral domains, von Neumann regular modules, Baer modules, quasi-regular modules, torsionfree modules, locally torsion-free modules, normal modules
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Marmara Üniversitesi Adresli:
Evet
Özet
© 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.