(b, c)-inverse, inverse along an element, and the Schützenberger category of a semigroup

Abstract

We prove that the (b, c)-inverse and the inverse along an element in a semigroup are actually genuine inverse when considered as morphisms in the Schützenberger category of a semigroup. Applications to the Reverse Order Law are given.

Keywords

• generalized inverses
• green’s relations
• reverse order law