The ideal structure of nilpotent-generated transformation semigroups

M.P.O. Marques-Smith, Robert Sullivan

    Research output: Contribution to journalArticle

    9 Citations (Scopus)

    Abstract

    In 1987 Sullivan determined the elements of the semigroup N(X) generated by all nilpotent partial transformations of an infinite set X; and later in 1997 he studied subsemigroups of N(X) defined by restricting the index of the nilpotents and the cardinality of the set. Here, we describe the ideals and Green's relations on such semigroups, like Reynolds and Sullivan did in 1985 for the semigroup generated by all idempotent total transformations of X. We then use this information to describe the congruences on certain Rees factor semigroups and to construct families of congruence-free semigroups with interesting algebraic properties. We also study analogous questions for X finite and for one-to-one partial transformations.
    Original languageEnglish
    Pages (from-to)303-318
    JournalBulletin of the Australian Mathematical Society
    Volume60
    DOIs
    Publication statusPublished - 1999

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