Epis, dominions and varieties of commutative posemigroups

Abstract

We show that the posemigroup dominion of a commutative posemigroup is again a commutative posemigroup and all varieties of commutative posemigroups are epimorphically closed. Next, we show that certain subvarieties of the variety of all commutative posemigroups are saturated. Finally, we show that a commutative posemigroup [Formula: see text] is saturated if [Formula: see text] is saturated for some positive integer [Formula: see text].