Inverse semigroup

Symbol-free definition
An inverse semigroup is a semigroup (i.e., a set with an associative binary operation) where every element has a unique inverse in the semigroup sense.

Definition with symbols
A semigroup $$(S,*)$$ is termed an inverse semigroup if for every $$a \in S$$, there is a unique $$c \in S$$ satisfying the conditions $$aca = a$$ and $$cac = c$$.

Stronger properties

 * Weaker than::Group
 * Weaker than::Clifford semigroup

Weaker properties

 * Stronger than::Regular semigroup