Maximal congruences on some semigroups

J. Sanwong, Robert Sullivan

    Research output: Contribution to journalArticlepeer-review

    6 Citations (Scopus)

    Abstract

    In 1976 Howie proved that a finite, congruence-free semigroup is a simple group if it has at least three elements but no zero element. Infinite congruence-free semigroups are far more complicated to describe, but some have been constructed using semigroups of transformations (for example, by Howie in 1981 and by Marques in 1983). Here, for certain semigroups S of numbers and of transformations, we determine all congruences rho on S such that S/rho is congruence-free, that is, we describe all maximal congruences on such semigroups S.
    Original languageEnglish
    Pages (from-to)255-263
    JournalAlgebra Colloquium
    Volume14
    Issue number2
    DOIs
    Publication statusPublished - 2007

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