Definition:Torsion Element

Definition

Torsion Element of Group

Let $G$ be a group.

An element of finite order of $G$ is also known as a torsion element of $G$.

Torsion Element of Module

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 $a m = 0$.