Saturated and epimorphically closed varieties of semigroups
Peter M. Higgins · Journal of the Australian Mathematical Society Series A Pure Mathematics and Statistics · 1984
Abstract We establish a necessary condition (E) for a semigroup variety to be closed under the taking of epimorphisms and a necessary condition (S) for a variety to consist entirely of saturated semigroups. Condition (S) is shown to be sufficient for heterotypical varieties and a stronger condition (S′) is shown to be sufficient for homotypical varieties.