- For the inverse of a relation, see Inverse (relation).
In abstract algebra, inverse of an element a, denoted as a', where a is an element of a set S in the monoid (S,·), is an element of S such that a·a' = e, where e is the identity element of (S,·).
If an inverse element exists for every element in a monoid (S,·), then the monoid is also a group.