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.
fusible ring fusible module torsion element torsion-free element
Fusible ring fusible module torsion element torsion-free element
Birincil Dil | İngilizce |
---|---|
Konular | Matematik |
Bölüm | Matematik |
Yazarlar | |
Erken Görünüm Tarihi | 14 Eylül 2023 |
Yayımlanma Tarihi | 27 Haziran 2024 |
Yayımlandığı Sayı | Yıl 2024 Cilt: 53 Sayı: 3 |