Fusible Modules

Yıl 2024, Erken Görünüm, 1 - 10

Işıl Baydar Burcu Üngör Sait Halicioglu Abdullah Harmancı

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

Öz

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 {\it 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 {\it fusible} if every non-zero element of $M$ is
fusible. We investigate some properties of fusible modules. It is
proved that the class fusible modules is situated between the
classes of torsion-free modules and nonsingular modules.

Anahtar Kelimeler

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

Kaynakça

• [1] E. Ghashghaei and W. Wm. McGovern, Fusible rings, Comm. Algebra 45 (3), 1151- 1165, 2017