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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.
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
Linking options:
https://www.mathnet.ru/eng/sm1983https://doi.org/10.1070/SM1985v051n01ABEH002846 https://www.mathnet.ru/eng/sm/v165/i1/p50
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Abstract page: | 333 | Russian version PDF: | 103 | English version PDF: | 4 | References: | 32 |
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