Definition:Torsion Element of Module

Definition

Let $R$ be a commutative ring with unity.

Let $M$ be a unitary module over $R$.

Let $m \in M$.

Then $m$ is a torsion element if and only if there exists a regular element $a \in R$ with $a m = 0$.

Also see

• Definition:Torsion-Free Module
• Definition:Torsion Submodule
• Definition:Torsion Element of Group