Definition:Torsion Module

Definition
Let $R$ be a commutative ring with unity.

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

Then $M$ is a torsion module every element of $M$ is of torsion, that is, $M$ equals its torsion submodule $T(M)$.

Also see

 * Definition:Torsion-Free Module
 * Definition:Torsion Group