Fusible modules

Year 2024, Volume: 53 Issue: 3, 714 - 723, 27.06.2024

Işıl Baydar , Burcu Üngör , Sait Halicioglu , Abdullah Harmancı

https://doi.org/10.15672/hujms.1206395

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.

Keywords

fusible ring, fusible module, torsion element, torsion-free element

References

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