Initial and Terminal Globalizations for Partial Actions of Inverse Semigroups

We study the globalization of partial actions from the viewpoint of universal constructions within specific classes of semigroups. Focusing on the important class of inverse semigroups, we construct two canonical globalizations for a strong partial action: an initial globalization via a modified tensor product and a terminal globalization via a Hom-set construction, both yielding global actions by inverse semigroups. We prove their universal properties and show that, unlike the group case, these objects are generally non- isomorphic. A concrete example based on the bicyclic monoid is provided to illustrate this distinction. Our work extends and refines the recent general theory of globalization for semigroup partial actions.

کلیدواژه ها:

Partial action ، Inverse semigroup ، Globalization ، Tensor product ، Universal property