Globalization of Partial Actions of Ordered Groupoids on Rings

Abstract: We provide a necessary and sufficient condition to the existence of an ordered globalization of a partial ordered action of an ordered groupoid on a ring and we also present criteria to obtain uniqueness. Furthermore, we apply those results to obtain a Morita context and to show that an inverse semigroup partial action has a globalization (unique up to isomorphism) if, and only if, it is unital.