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Fundam. Prikl. Mat., 2006, Volume 12, Issue 8, Pages 97–104 (Mi fpm30)  

This article is cited in 8 scientific papers (total in 8 papers)

Regularity conditions for semigroups of isotone transformations of countable chains

V. I. Kim, I. B. Kozhukhov

Moscow State Institute of Electronic Technology (Technical University)

Abstract: Let $\Gamma$ be a linearly ordered set (a chain), $O(\Gamma)$ be the semigroup of all isotone transformations of $\Gamma$ (i.e., order-preserving transformations). We find some necessary and some sufficient conditions on the chain $\Gamma$ for the semigroup $O(\Gamma)$ to be regular. For example, if $\Gamma$ is a complete chain with the maximal element and the minimal one, then $O(\Gamma)$ is regular. In particular, $O(\Gamma)$ is regular if $\Gamma$ is finite. We find necessary and sufficient conditions for the regularity of $O(\Gamma)$ in the case where $\Gamma$ is countable.

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English version:
Journal of Mathematical Sciences (New York), 2008, 152:2, 203–208

Bibliographic databases:

UDC: 512.534.5

Citation: V. I. Kim, I. B. Kozhukhov, “Regularity conditions for semigroups of isotone transformations of countable chains”, Fundam. Prikl. Mat., 12:8 (2006), 97–104; J. Math. Sci., 152:2 (2008), 203–208

Citation in format AMSBIB
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\paper Regularity conditions for semigroups of isotone transformations of countable chains
\jour Fundam. Prikl. Mat.
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\pages 97--104
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\transl
\jour J. Math. Sci.
\yr 2008
\vol 152
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\pages 203--208
\crossref{https://doi.org/10.1007/s10958-008-9063-x}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. I. Kim, I. B. Kozhukhov, “On semigroups of isotonic transformations of partially ordered sets”, Russian Math. Surveys, 62:5 (2007), 996–998  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. Yu. V. Zhuchok, “Endomorphism semigroups of 2-nilpotent binary relations”, J. Math. Sci., 164:1 (2010), 49–55  mathnet  crossref  mathscinet  elib
    3. Yaroshevich V.A., “O svoistvakh polugrupp chastichnykh izotonnykh preobrazovanii kvaziuporyadochennykh mnozhestv”, Vestnik Moskovskoi gosudarstvennoi akademii delovogo administrirovaniya. Seriya: Filosofskie, sotsialnye i estestvennye nauki, 2011, no. 3, 139–144  elib
    4. 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
    5. Yaroshevich V.A., “O regulyarnykh polugruppakh izotonnykh preobrazovanii chastichno uporyadochennykh mnozhestv”, Vestnik moskovskoi gosudarstvennoi akademii delovogo administrirovaniya. seriya: ekonomika, 2012, no. 4, 130–134  elib
    6. Yu. V. Zhuchok, E. A. Toichkina, “The endotopism semigroups of an equivalence relation”, Sb. Math., 205:5 (2014), 646–662  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. E. A. Bondar, “O regulyarnosti nekotorykh podpolugrupp monoida endomorfizmov otnosheniya ekvivalentnosti”, PDM, 2014, no. 3(25), 5–11  mathnet
    8. Fernandes V.H., Honyam P., Quinteiro T.M., Singha B., “on Semigroups of Endomorphisms of a Chain With Restricted Range”, Semigr. Forum, 89:1 (2014), 77–104  crossref  mathscinet  zmath  isi
  • Фундаментальная и прикладная математика
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