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Sbornik: Mathematics, 2014, Volume 205, Issue 5, Pages 646–662
DOI: https://doi.org/10.1070/SM2014v205n05ABEH004392 (Mi sm8325) 		 
This article is cited in 5 scientific papers (total in 5 papers)

The endotopism semigroups of an equivalence relation

Yu. V. Zhuchoka, E. A. Toichkinab

a National Taras Shevchenko University of Kyiv
b Lugansk Taras Shevchenko National University
English version PDF (473 kB) Citations (5) Russian version article
References:
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DOI: https://doi.org/10.1070/SM2014v205n05ABEH004392
Abstract: In this work we investigate six types of endotopism semigroups for a given equivalence relation. Necessary and sufficient conditions for the existence of all such endotopisms are presented. Conditions for the regularity and coregularity of each of the endotopism semigroups of a given type are established. The notion of the endotype of a binary relation with respect to its endotopisms is introduced and the endotype of an arbitrary equivalence relation is calculated.
Bibliography: 26 titles.
Keywords: endotopism, equivalence relation, regularity, coregularity, endotype.
Received: 13.01.2014
Bibliographic databases:
Document Type: Article
UDC: 512.53
MSC: 20M20
Language: English
Original paper language: Russian
Citation: Yu. V. Zhuchok, E. A. Toichkina, “The endotopism semigroups of an equivalence relation”, Sb. Math., 205:5 (2014), 646–662
Citation in format AMSBIB
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\by Yu.~V.~Zhuchok, E.~A.~Toichkina
\paper The endotopism semigroups of an equivalence relation
\jour Sb. Math.
\yr 2014
\vol 205
\issue 5
\pages 646--662
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Linking options:
  • https://www.mathnet.ru/eng/sm8325
  • https://doi.org/10.1070/SM2014v205n05ABEH004392
  • https://www.mathnet.ru/eng/sm/v205/i5/p37
    • This publication is cited in the following 5 articles:
    1. Yu. Zhuchok, O. Toichkina, “Napіvgrupa slabkikh endomorfіzmіv vіdnoshennya chastkovoï ekvіvalentnostі”, Ukr. Mat. Zhurn., 76:12 (2024)  crossref
    2. Yu. V. Zhuchok, E. A. Toichkina, “The endotopism semigroups of a partial equivalence relation”, Siberian Math. J., 62:6 (2021), 1039–1049  mathnet  crossref  crossref  isi  elib
    3. Zhuchok Yu. Toichkina O., “Endotypes of Partial Equivalence Relations”, Semigr. Forum, 103:3 (2021), 966–975  crossref  mathscinet  isi
    4. E. A. Toichkina, “Semigroups of endotopisms of effective connected relations”, Ukr. Math. J., 68:3 (2016), 422–432  crossref  mathscinet  zmath  isi  scopus
    5. Yu. V. Zhuchok, E. A. Toichkina, “Correspondences of the Semigroup of Endomorphisms of an Equivalence Relation”, Math. Notes, 97:2 (2015), 201–212  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математический сборник Sbornik: Mathematics
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    Abstract page:686
    Russian version PDF:274
    English version PDF:22
    References:81
    First page:28
     
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