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Transformation semigroups preserving a binary relation

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Abstract

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

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Authors and Affiliations

  1. Moscow Institute of Electronic Engineering, Moscow, Russia

    I. B. Kozhukhov & V. A. Yaroshevich

Authors
  1. I. B. Kozhukhov
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  2. V. A. Yaroshevich
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Correspondence to I. B. Kozhukhov.

Additional information

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 14, No. 7, pp. 129–135, 2008.

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Kozhukhov, I.B., Yaroshevich, V.A. Transformation semigroups preserving a binary relation. J Math Sci 164, 240–244 (2010). https://doi.org/10.1007/s10958-009-9723-5

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  • DOI: https://doi.org/10.1007/s10958-009-9723-5

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