Abstract
Given a semilattice Y of inverse semigroups Sα, there corresponds a semilattice Y of groups Gα in a natural way. This correspondence is used to study semilattices of proper inverse semigroups. In paticular, it is shown that if S is a semilattice of proper inverse semigroups, then there exists a minimum semilattice congruence η such that each η-class is proper and there exists a maximum semilattice congruence ν such that each ν-class is proper.
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Communicated by Robert McFadden
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Hardy, D.W., Tirasupa, Y. Semilattices of proper inverse semigroups. Semigroup Forum 13, 29–36 (1976). https://doi.org/10.1007/BF02194919
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DOI: https://doi.org/10.1007/BF02194919