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Ordered sets and their inf-endomorphisms

  • Yu. M. Vazhenin
Article
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Abstract

From the semigroup of all transformations of an ordered set is selected the class of subsets such that the structure of each of them, as a partially ordered groupoid, comprehensively characterizes the degree of order of the given set, with the exception of the case when it consists of two elements.

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Literature cited

  1. 1.
    A. Ya. Aizenshtat, “A class of semigroups of endomorphisms of ordered sets,” VIII Vsesoyuznyi Kollokvium po Obshchei Algebre, Rezyume Coobshch. i Dokl., 3–4 (1967).Google Scholar
  2. 2.
    L. M. Gluskin, “Semigroups of isotonic transformations,” Uspekh. Matem. Nauk,16, No. 5, 157–162 (1961).Google Scholar
  3. 3.
    L. B. Shneperman, “Semigroups of endomorphisms of quasi-ordered sets,” Uchen. Zap. Leningr. Ped. In-ta, 238, 21–37 (1962).Google Scholar

Copyright information

© Consultants Bureau 1970

Authors and Affiliations

  • Yu. M. Vazhenin
    • 1
  1. 1.A. M. Gor'kii Urals State UniversityUSSR

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