Completions of Generalized Restriction P-Restriction Semigroups

Abstract

Generalized restriction P-restriction semigroups are common generalizations of restriction semigroups and generalized inverse $$*$$ -semigroups. Gomes and Szendrei (resp. Ohta and Imaoka) have shown that every restriction semigroup (every generalized inverse $$*$$ -semigroup) can be embedded in a complete, infinitely distributive restriction semigroup (resp. a $$*$$ -complete, infinitely distributive generalized inverse $$*$$ -semigroup). The main aim of this paper is to obtain an entirely corresponding result for generalized restriction P-restriction semigroups. Specifically, among other things, we show that every generalized restriction P-restriction semigroup can be (2,1,1)-embedded in a complete, infinitely distributive generalized restriction P-restriction semigroup. Our results generalize and enrich the corresponding results of Gomes, Szendrei, Ohta and Imaoka.