Epimorphisms, dominions and H-commutative semigroups

Abstract

In the present paper, a series of results and examples that explore the structural features of H-commutative semigroups are provided. We also generalise a result of Isbell from commutative semigroups to H-commutative semigroups by showing that the dominion of an H-commutative semigroup is H-commutative. We then use this to generalise Howie and Isbell's result that any H-commutative semigroup satisfying the minimum condition on principal ideals is saturated.