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Algebra Discrete Math., 2009, Issue 2, Pages 116–127 (Mi adm124)  

This article is cited in 17 scientific papers (total in 17 papers)

RESEARCH ARTICLE

Commutative dimonoids

A. V. Zhuchok

Department of Mechanics and Mathematics, Kyiv National Taras Shevchenko University, Volodymyrska str., 64, 01033 Kyiv, Ukraine

Abstract: We present some congruence on the dimonoid with a commutative operation and use it to obtain a decomposition of a commutative dimonoid.

Keywords: dimonoid with a commutative operation, commutative dimonoid, semilattice of dimonoids.

Full text: PDF file (220 kB)

Bibliographic databases:
MSC: 08A05
Received: 18.11.2008
Revised: 26.07.2009
Language:

Citation: A. V. Zhuchok, “Commutative dimonoids”, Algebra Discrete Math., 2009, no. 2, 116–127

Citation in format AMSBIB
\Bibitem{Zhu09}
\by A.~V.~Zhuchok
\paper Commutative dimonoids
\jour Algebra Discrete Math.
\yr 2009
\issue 2
\pages 116--127
\mathnet{http://mi.mathnet.ru/adm124}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2589078}
\zmath{https://zbmath.org/?q=an:1199.08004}


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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. Zhuchok A.V., “Free Dimonoids”, Ukr. Math. J., 63:2 (2011), 196–208  crossref  mathscinet  zmath  isi  elib  scopus
    2. Anatolii V. Zhuchok, “Free rectangular dibands and free dimonoids”, Algebra Discrete Math., 11:2 (2011), 92–111  mathnet  mathscinet  zmath
    3. Anatolii V. Zhuchok, “Free normal dibands”, Algebra Discrete Math., 12:2 (2011), 112–127  mathnet  mathscinet  zmath
    4. A. V. Zhuchok, “Dimonoids”, Algebra and Logic, 50:4 (2011), 323–340  mathnet  crossref  mathscinet  zmath  isi
    5. Anatolii V. Zhuchok, “Semilattices of $r$-archimedean subdimonoids”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2011, no. 3, 108–112  mathnet  mathscinet  zmath
    6. A. V. Zhuchok, “Some congruences on trioids”, J. Math. Sci., 187:2 (2012), 138–145  mathnet  crossref
    7. A. V. Zhuchok, “Dekompozitsii svobodnykh dimonoidov”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 154, no. 2, Izd-vo Kazanskogo un-ta, Kazan, 2012, 93–100  mathnet
    8. A. V. Zhuchok, “Free $n$-nilpotent dimonoids”, Algebra Discrete Math., 16:2 (2013), 299–310  mathnet  mathscinet
    9. A. V. Zhuchok, “Dimonoids and bar-units”, Siberian Math. J., 56:5 (2015), 827–840  mathnet  crossref  crossref  isi  elib  elib
    10. Anatolii V. Zhuchok, Milan Demko, “Free $n$-dinilpotent doppelsemigroups”, Algebra Discrete Math., 22:2 (2016), 304–316  mathnet  mathscinet
    11. Zhuchok A.V., Gorbatkov A.B., “on the Structure of Dimonoids”, Semigr. Forum, 94:2 (2017), 194–203  crossref  mathscinet  zmath  isi  scopus
    12. Zhuchok A.V., “Structure of Relatively Free Dimonoids”, Commun. Algebr., 45:4 (2017), 1639–1656  crossref  mathscinet  zmath  isi  scopus
    13. Zhuchok A.V., “Free Products of Doppelsemigroups”, Algebr. Universalis, 77:3 (2017), 361–374  crossref  mathscinet  zmath  isi  scopus
    14. Zhuchok A.V., “Free Left N-Dinilpotent Doppelsemigroups”, Commun. Algebr., 45:11 (2017), 4960–4970  crossref  mathscinet  zmath  isi  scopus
    15. A. V. Zhuchok, “Free $n$-Tuple Semigroups”, Math. Notes, 103:5 (2018), 737–744  mathnet  crossref  crossref  isi  elib
    16. Anatolii V. Zhuchok, Kolja Knauer, “Abelian doppelsemigroups”, Algebra Discrete Math., 26:2 (2018), 290–304  mathnet
    17. Zhuchok A.V., “Structure of Free Strong Doppelsemigroups”, Commun. Algebr., 46:8 (2018), 3262–3279  crossref  mathscinet  zmath  isi  scopus
  • Algebra and Discrete Mathematics
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