Fusible modules

Authors : Işıl Baydar, Burcu Üngör, Sait Halicioglu, Abdullah Harmancı

Pages : 714-723

Doi:10.15672/hujms.1206395

View : 324 | Download : 893

Publication Date : 2024-06-27

Article Type : Research Paper

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