Let be a Module over a ring .
A torsion element is an element that yields zero when multiplied by some non-Zero-divisor, i.e. .
This is a strong deviation from the behaviour of a vector space,
as torsion elements cannot exist for a module over a field,
where scalar multiplication is injective,
hence vector spaces are torsion-free.
A torsion module consists of only torsion elements.
Given a module, the set of all torsion elements forms the Torsion submodule.