Fusible Modules

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 {\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.