Global determinism of semigroups having regular globals

Abstract

The aim of this paper is to study the global determinism of the class ${\mathcal {A}}$ of all semigroups having regular globals. It is known from PeliKán (Periodica Math Hungarica 4:103–106, 1973) and Pondělíček (On semigroups having regular globals, 1976) that ${\mathcal {A}}$ can be divided into two subclasses: the class ${\mathcal {A}}_{2}$ of all semigroups having idempotent globals and the class ${\mathcal {A}}_{3}$ of all semigroups having regular but non-idempotent globals. We prove that ${\mathcal {A}}_{2}$ is globally determined and that ${\mathcal {A}}_{3}$ satisfies the strong isomorphism property. This shows that ${\mathcal {A}}$ is globally determined.