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Algebra Discrete Math., 2011, Volume 11, Issue 2, Pages 92–111 (Mi adm14)  

This article is cited in 12 scientific papers (total in 12 papers)

RESEARCH ARTICLE

Free rectangular dibands and free dimonoids

Anatolii V. Zhuchok

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

Abstract: We construct a free rectangular diband and describe its structure. We also present the least rectangular diband congruence, the least $(rb,rz)$-congruence, the least left zero and right zero congruence, the least rectangular band congruence and the least left zero congruence on free dimonoids and use them to obtain decompositions of free dimonoids.

Keywords: rectangular dimonoid, free rectangular dimonoid, free dimonoid, diband of subdimonoids.

Full text: PDF file (280 kB)
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Bibliographic databases:
MSC: 08B20, 20M10, 20M50, 17A30, 17A32
Received: 23.02.2011
Revised: 27.05.2011
Language:

Citation: Anatolii V. Zhuchok, “Free rectangular dibands and free dimonoids”, Algebra Discrete Math., 11:2 (2011), 92–111

Citation in format AMSBIB
\Bibitem{Zhu11}
\by Anatolii V. Zhuchok
\paper Free rectangular dibands and free dimonoids
\jour Algebra Discrete Math.
\yr 2011
\vol 11
\issue 2
\pages 92--111
\mathnet{http://mi.mathnet.ru/adm14}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2858132}
\zmath{https://zbmath.org/?q=an:06120606}


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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. Anatolii V. Zhuchok, “Free normal dibands”, Algebra Discrete Math., 12:2 (2011), 112–127  mathnet  mathscinet  zmath
    2. Anatolii V. Zhuchok, “Semilattices of $r$-archimedean subdimonoids”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2011, no. 3, 108–112  mathnet  mathscinet  zmath
    3. 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
    4. A. V. Zhuchok, “Cvobodnye $n$-dinilpotentnye dimonoidy”, PFMT, 2013, no. 4(17), 43–46  mathnet
    5. A. V. Zhuchok, “Free $(\ell r, rr)$-dibands”, Algebra Discrete Math., 15:2 (2013), 295–304  mathnet  mathscinet
    6. A. V. Zhuchok, “Free $n$-nilpotent dimonoids”, Algebra Discrete Math., 16:2 (2013), 299–310  mathnet  mathscinet
    7. A. V. Zhuchok, “Dimonoids and bar-units”, Siberian Math. J., 56:5 (2015), 827–840  mathnet  crossref  crossref  isi  elib  elib
    8. Yuliia V. Zhuchok, “Free rectangular tribands”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2015, no. 2, 61–73  mathnet
    9. A. Zhuchok, Yu. Zhuchok, “Free left $n$-dinilpotent dimonoids”, Semigr. Forum, 93:1 (2016), 161–179  crossref  mathscinet  zmath  isi  scopus
    10. Zhuchok A.V., “Structure of Relatively Free Dimonoids”, Commun. Algebr., 45:4 (2017), 1639–1656  crossref  mathscinet  zmath  isi  scopus
    11. A. V. Zhuchok, “Free $n$-Tuple Semigroups”, Math. Notes, 103:5 (2018), 737–744  mathnet  crossref  crossref  isi  elib
    12. Anatolii V. Zhuchok, Kolja Knauer, “Abelian doppelsemigroups”, Algebra Discrete Math., 26:2 (2018), 290–304  mathnet
  • Algebra and Discrete Mathematics
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