For questions about inverse semigroups, Clifford semigroups and other classes of semigroups with the notion of inverses from semigroup theory. Use in conjunction with the tag (semigroups).
An inverse semigroup is a (regular) semigroup with the notion of unique inverses. So, it consists of a triple $(S, \cdot, \star),$ where $S$ is a non-empty set $\cdot :S\times S\to C$ is an associative binary operation and $\star : S\to S$ is an involutive unary operation satisfying $aa^{\star}a=a^{\star}, a^{\star}aa^{\star}=a^{\star}$ for all $a\in S.$ The uniqueness of inverses distinguish inverse semigroups form regular semigroups while adding more nice properties to the structure. For example in an inverse semigroup, idempotents commute with each others. Vagner-Preston representation tells that every inverse semigroup is a sub-semigroup of partial bijections on some set.
