Epimorphisms, Dominions, and Various Classes of Saturated Semigroups

Abstract

In this paper, we discussed some saturated classes of $\mathrm{\mathscr{H}}$ -commutative semigroups, left (right) regular semigroups, medial semigroups, and paramedial semigroups. The results of this paper significantly extend the long standing result about normal bands that normal bands were saturated and, thus, significantly broaden the class of saturated semigroups.