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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
It is proved that the class of fusible modules is between the classes of torsion-free and nonsingular modules.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, we extend the concept of fusibility to the module-theoretic setting by introducing fusible modules.
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Key Findings & Data:Let $R$ be a ring with identity, $M$ a right $R$-module and $0\neq m\in M$.
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Conclusion & Impact:It is proved that the class of fusible modules is between the classes of torsion-free and nonsingular modules.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:fusible ring · fusible module · torsion element
Abstract
In this paper, we extend the concept of fusibility to the module-theoretic setting by introducing fusible modules. Let $R$ be a ring with identity, $M$ a right $R$-module and $0\neq m\in M$. Then, $m$ is called fusible if it can be expressed as the sum of a torsion element and a torsion-free element in $M$. The module $M$ is said to be fusible if every non-zero element of $M$ is fusible. We investigate some properties of fusible modules. It is proved that the class of fusible modules is between the classes of torsion-free and nonsingular modules.
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Cite This Article
Baydar, I., Üngör, B., Halicioglu, S., Harmancı, A. (2024). Fusible modules. Hacettepe Journal of Mathematics and Statistics, Volume: 53 Issue: 3. https://doi.org/10.15672/hujms.1206395