Definition:Inverse Semigroup

Definition
An inverse semigroup is a semigroup $\left({S, \circ}\right)$ such that:


 * $\forall a \in S: \exists! b \in S: a = a \circ b \circ a, b = b \circ a \circ b$

The element $b$ is called the inverse of $a$. By definition, it is unique.

Also see

 * Group is Inverse Semigroup