The congruences on the semigroup of balanced transformations of an infinite set

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

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    Abstract

    In 1966, J. M. Howie (J. London Math. Sec. 41, 707-716) showed that the semigroup generated by all non-identity idempotent transformations of an infinite set X is the disjoint union of two semigroups, one of which is denoted by H and consists of all balanced transformations of X (that is, all transformations whose defect, shift, and collapse are equal and infinite). Subsequently, J. M. Howie (1981, Proc. Roy Sec. Edinburgh Sect. A 88, 159-167, 169-184) and Marques (1983, Proc. Roy. Sec. Edinburgh Sect. A 93, 245-257) showed that certain Rees quotient semigroups associated with H are congruence-free. Here, we describe all congruences on H. (C) 2000 Academic Press.
    Original languageEnglish
    Pages (from-to)1-30
    JournalJournal of Algebra
    Volume234
    DOIs
    Publication statusPublished - 2000

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