Clifford semigroup

A Clifford semigroup (sometimes also called "inverse Clifford semigroup") is a completely regular inverse semigroup. It is an inverse semigroup with x x − 1 = x − 1 x . Examples of Clifford semigroups are groups and commutative inverse semigroups.

In a Clifford semigroup, x y = y x ↔ x − 1 y = y x − 1 .