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    Saturated and epimorphically closed varieties of semigroups
    Journal of the Australian Mathematical Society Series A Pure Mathematics and Statistics (1984)
    Peter M. Higgins
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    Abstract:
    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.
    Topics:
    semigroups and automata theory
    Geometric and Algebraic Topology
    Fuzzy and Soft Set Theory
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