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Characterizations of totally ordered sets by their various endomorphisms

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Abstract

We characterize totally ordered sets within the class of all ordered sets containing at least three-element chains using a simple relationship between their isotone transformations and the so called 2-, 3-, 4-endomorphisms which are introduced in the paper. Another characterization of totally ordered sets within the class of ordered sets of a locally finite height with at least four-element chains in terms of the regular semigroup theory is also given.

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Authors and Affiliations

  1. Katedra algebry a geometrie PřF UP, Tomkova 40, 779 00, Olomouc, Czech Republic

    Daniel Hort

  2. Katedra matematiky PdF MU, Poříčí 31, 603 00, Brno, Czech Republic

    Jan Chvalina

  3. VVŠ-PV, Katedra matematiky, 682 02, Vyškov, Czech Republic

    Jiří Moučka

Authors
  1. Daniel Hort
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  2. Jan Chvalina
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  3. Jiří Moučka
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Hort, D., Chvalina, J. & Moučka, J. Characterizations of totally ordered sets by their various endomorphisms. Czechoslovak Mathematical Journal 52, 23–32 (2002). https://doi.org/10.1023/A:1021763102781

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