On Regular Fusible Modules
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866916169807560704 |
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| author | Naji, Osama A. Özen, Mehmet Tekir, Ünsal Koç, Suat |
| author_facet | Naji, Osama A. Özen, Mehmet Tekir, Ünsal Koç, Suat |
| contents | In this article, we introduce the notion of regular fusible modules. Let $R$ be a ring with an identity and $M$ an $R$-module. An element $0\neq m\in M$ is said to be regular fusible if there exists $r\in R$, a non zero-divisor of $M$, such that $mr$ can be written as the sum of a torsion element and a torsion free element in $M$. $M$ is called regular fusible if every nonzero element of $M$ is regular fusible. We characterize regular fusible modules in terms of fusible modules. In addition, we show that a regular fusible module over a right duo ring is reduced and nonsingular. Moreover, we study the regular fusible property under Cartesian product, trivial extension ring, and module of a fractions. Also, we characterize division rings in terms of fusible modules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_13939 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Regular Fusible Modules Naji, Osama A. Özen, Mehmet Tekir, Ünsal Koç, Suat Rings and Algebras Commutative Algebra 16D10, 16D80, 16U99 In this article, we introduce the notion of regular fusible modules. Let $R$ be a ring with an identity and $M$ an $R$-module. An element $0\neq m\in M$ is said to be regular fusible if there exists $r\in R$, a non zero-divisor of $M$, such that $mr$ can be written as the sum of a torsion element and a torsion free element in $M$. $M$ is called regular fusible if every nonzero element of $M$ is regular fusible. We characterize regular fusible modules in terms of fusible modules. In addition, we show that a regular fusible module over a right duo ring is reduced and nonsingular. Moreover, we study the regular fusible property under Cartesian product, trivial extension ring, and module of a fractions. Also, we characterize division rings in terms of fusible modules. |
| title | On Regular Fusible Modules |
| topic | Rings and Algebras Commutative Algebra 16D10, 16D80, 16U99 |
| url | https://arxiv.org/abs/2403.13939 |