torsion (module theory)

Definition

For a ring and a module , an element is torsion if for some .

If is commutative then the subset consisting of torsion elements is called the torsion submodule. Note if is not commutative, then this set is not a submodule.

Examples

• For a field, then any -module is just a vector space and the only torsion element is .

• The torsion elements of any -module are elements of finite order.