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Fundam. Prikl. Mat., 2008, Volume 14, Issue 7, Pages 129–135 (Mi fpm1177)  

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

Transformation semigroups preserving a binary relation

I. B. Kozhukhov, V. A. Yaroshevich

Moscow State Institute of Electronic Technology

Abstract: We investigate the semigroups of full and partial transformations of a set $X$ which preserve a binary relation $\sigma$ defined on $X$. We consider in detail the case where $\sigma$ is an order or a quasi-order relation. There are conditions of regularity of such semigroups. We introduce two definitions of preservation of $\sigma$ for the semigroup of binary relations. It is proved that subsets of $\mathrm B(X)$ preserving $\sigma$ are semigroups in each case. We give the condition of regularity of $\mathrm B_\sigma(X)$ in the case where $\sigma(X)$ is a quasi-order.

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English version:
Journal of Mathematical Sciences (New York), 2010, 164:2, 240–244

Bibliographic databases:

UDC: 512.562

Citation: I. B. Kozhukhov, V. A. Yaroshevich, “Transformation semigroups preserving a binary relation”, Fundam. Prikl. Mat., 14:7 (2008), 129–135; J. Math. Sci., 164:2 (2010), 240–244

Citation in format AMSBIB
\Bibitem{KozYar08}
\by I.~B.~Kozhukhov, V.~A.~Yaroshevich
\paper Transformation semigroups preserving a~binary relation
\jour Fundam. Prikl. Mat.
\yr 2008
\vol 14
\issue 7
\pages 129--135
\mathnet{http://mi.mathnet.ru/fpm1177}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2533601}
\elib{http://elibrary.ru/item.asp?id=12291803}
\transl
\jour J. Math. Sci.
\yr 2010
\vol 164
\issue 2
\pages 240--244
\crossref{https://doi.org/10.1007/s10958-009-9723-5}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-71649113953}


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    This publication is cited in the following articles:
    1. 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
    2. E. A. Bondar, “O regulyarnosti nekotorykh podpolugrupp monoida endomorfizmov otnosheniya ekvivalentnosti”, PDM, 2014, no. 3(25), 5–11  mathnet
  • Фундаментальная и прикладная математика
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