Global determinism of semigroups having regular globals

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 Pondělí?ek (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.