On saturated varieties of posemigroups

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].…”

“…Let U be a semigroup fulfilling the identity xy � xy2 and let S be a semigroup containing U as a proper subsemigroup and such that Dom(U, S) � S. en xay � xa 2 y for all a ∈ U and x, y ∈ S.Proof. If x ∈ S, then the proof follows trivially.…”