An automorphism theorem on certain type B semigroups

Abstract

Motivated by studying translational hulls in semigroups and rings, and also motivated M.  Petrich and J. E. Ault’s works in inverse semigroups in terms of translational hulls, we attempt in this article to study the idempotents of the translational hull of a type B semigroup.  Our main result is to prove that the idempotent set of the translational hull of an arbitrary type B semigroup is isomorphic to the translational hull of the idempotent set of such a semigroup.