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].

Epimorphisms, Dominions, and Various Classes of Saturated Semigroups

“…e following semigroups are not saturated: commutative cancellative semigroups, subsemigroups of finite inverse semigroups [17], commutative periodic semigroups [14], and bands, since Trotter [24] has produced a band with a correctly epimorphically embedded subband. In this direction, a very recent significant and remarkable work have been made by Ahanger and Shah on partially ordered semigroups (posemigroups), and commutative posemigroups (see [1][2][3], [23]). Now, we begin with the class of H-commutative semigroups whose concept was first developed by Tully [25].…”