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Mat. Sb. (N.S.), 1984, Volume 123(165), Number 1, Pages 50–68 (Mi msb1983)  

This article is cited in 2 scientific papers (total in 2 papers)

On monoids of isotone mappings

L. A. Skornyakov


Abstract: The author introduces a class $\mathfrak D$ of sufficient monoids which are monoids isomorphic to certain special submonoids of monoids of isotone selfmaps of partially ordered sets with a greatest or least element. In contradistinction to the class of monoids isomorphic to monoids of all isotone maps, $\mathfrak D$ is an axiomatizable class. It follows from the isomorphism [elementary equivalence] of sufficient monoids of partially ordered sets $P$ and $P'$ that $P'$ is isomorphic [elementarily equivalent] to either $P$ or $P^{\mathrm{op}}$. Elementarily equivalent partially ordered sets possess elementarily equivalent sufficient monoids.
Figures: 2.
Bibliography: 19 titles.

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English version:
Mathematics of the USSR-Sbornik, 1985, 51:1, 47–65

Bibliographic databases:

UDC: 512.562
MSC: Primary 20M20; Secondary 06A10
Received: 08.02.1983

Citation: L. A. Skornyakov, “On monoids of isotone mappings”, Mat. Sb. (N.S.), 123(165):1 (1984), 50–68; Math. USSR-Sb., 51:1 (1985), 47–65

Citation in format AMSBIB
\Bibitem{Sko84}
\by L.~A.~Skornyakov
\paper On monoids of isotone mappings
\jour Mat. Sb. (N.S.)
\yr 1984
\vol 123(165)
\issue 1
\pages 50--68
\mathnet{http://mi.mathnet.ru/msb1983}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=728929}
\zmath{https://zbmath.org/?q=an:0581.20063}
\transl
\jour Math. USSR-Sb.
\yr 1985
\vol 51
\issue 1
\pages 47--65
\crossref{https://doi.org/10.1070/SM1985v051n01ABEH002846}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. I. Kim, I. B. Kozhukhov, “Regularity conditions for semigroups of isotone transformations of countable chains”, J. Math. Sci., 152:2 (2008), 203–208  mathnet  crossref  mathscinet  zmath  elib  elib
    2. V. I. Kim, I. B. Kozhukhov, V. A. Yaroshevich, “Weakly regular semigroups of isotone transformations”, J. Math. Sci., 191:5 (2013), 694–708  mathnet  crossref
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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