Congruences on Semigroups generated by Injective Nilpotent Transformations

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

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    Abstract

    In 1987, Sullivan characterised the elements of the semigroup NI(X) generated by the nilpotents in I(X), the symmetric inverse semigroup on an infinite set X, and, in the same year, Gomes and Howie did the same for finite X. In 1999, Marques-Smith and Sullivan determined all the ideals of NI(X) for axbitrary X. In this paper, we use that work to describe all the congruences on NI(X).
    Original languageEnglish
    Pages (from-to)393-409
    JournalBulletin of the Australian Mathematical Society
    Volume74
    Issue number3
    Publication statusPublished - 2006

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