Maximal and Minimal Congruences on some Semigroups

J. Sanwong, B. Singha, Robert Sullivan

    Research output: Contribution to journalArticlepeer-review

    17 Citations (Scopus)

    Abstract

    In 2006, Sanwong and Sullivan described the maximal congruences on the semigroup N consisting of all non-negative integers under standard multiplication, and on the semigroup T(X) consisting of all total transformations of an infinite set X under composition. Here, we determine all maximal congruences on the semigroup ℤ n under multiplication modulo n. And, when Y ⊆ X, we do the same for the semigroup T(X, Y) consisting of all elements of T(X) whose range is contained in Y. We also characterise the minimal congruences on T(X, Y).
    Original languageEnglish
    Pages (from-to)455-466
    JournalActa Mathematica Sinica-English Series
    Volume25
    Issue number3
    DOIs
    Publication statusPublished - 2009

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