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Algebra Discrete Math., 2010, Volume 9, Issue 1, Pages 109–119 (Mi adm24)  

This article is cited in 23 scientific papers (total in 23 papers)

RESEARCH ARTICLE

Free commutative dimonoids

Anatolii V. Zhuchok

National Taras Shevchenko University of Kyiv, The Faculty of Mechanics and Mathematics

Abstract: We construct a free commutative dimonoid and characterize the least idempotent congruence on this dimonoid.

Keywords: commutative dimonoid, free commutative dimonoid.

Full text: PDF file (214 kB)

Bibliographic databases:
MSC: 08A05
Received: 15.09.2009
Revised: 30.04.2010
Language:

Citation: Anatolii V. Zhuchok, “Free commutative dimonoids”, Algebra Discrete Math., 9:1 (2010), 109–119

Citation in format AMSBIB
\Bibitem{Zhu10}
\by Anatolii V. Zhuchok
\paper Free commutative dimonoids
\jour Algebra Discrete Math.
\yr 2010
\vol 9
\issue 1
\pages 109--119
\mathnet{http://mi.mathnet.ru/adm24}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2681186}
\zmath{https://zbmath.org/?q=an:1224.08002}


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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, “Cvobodnye $n$-dinilpotentnye dimonoidy”, PFMT, 2013, no. 4(17), 43–46  mathnet
    9. A. V. Zhuchok, “Free $(\ell r, rr)$-dibands”, Algebra Discrete Math., 15:2 (2013), 295–304  mathnet  mathscinet
    10. A. V. Zhuchok, “Free $n$-nilpotent dimonoids”, Algebra Discrete Math., 16:2 (2013), 299–310  mathnet  mathscinet
    11. Yuri Movsisyan, Sergey Davidov, Mher Safaryan, “Construction of free $\mathfrak{g}$-dimonoids”, Algebra Discrete Math., 18:1 (2014), 138–148  mathnet  mathscinet
    12. A. V. Zhuchok, Yu. V. Zhuchok, “Free commutative $g$-dimonoids”, Chebyshevskii sb., 16:3 (2015), 276–284  mathnet  elib
    13. A. V. Zhuchok, “Dimonoids and bar-units”, Siberian Math. J., 56:5 (2015), 827–840  mathnet  crossref  crossref  isi  elib  elib
    14. Yurii V. Zhuchok, “Free abelian dimonoids”, Algebra Discrete Math., 20:2 (2015), 330–342  mathnet  mathscinet
    15. Smith J.D.H., “Directional Algebras”, Houst. J. Math., 42:1 (2016), 1–22  mathscinet  zmath  isi
    16. Zhang G., Chen Yu., “a New Composition-Diamond Lemma For Dialgebras”, Algebr. Colloq., 24:2 (2017), 323–350  crossref  mathscinet  zmath  isi  scopus
    17. Zhuchok Yu.V., “Automorphisms of the Endomorphism Semigroup of a Free Commutative Dimonoid”, Commun. Algebr., 45:9 (2017), 3861–3871  crossref  mathscinet  zmath  isi  scopus
    18. Zhuchok A.V., “Structure of Relatively Free Dimonoids”, Commun. Algebr., 45:4 (2017), 1639–1656  crossref  mathscinet  zmath  isi  scopus
    19. Zhuchok A.V., “Free Products of Doppelsemigroups”, Algebr. Universalis, 77:3 (2017), 361–374  crossref  mathscinet  zmath  isi  scopus
    20. Zhuchok A.V., “Free Left N-Dinilpotent Doppelsemigroups”, Commun. Algebr., 45:11 (2017), 4960–4970  crossref  mathscinet  zmath  isi  scopus
    21. A. V. Zhuchok, “Free $n$-Tuple Semigroups”, Math. Notes, 103:5 (2018), 737–744  mathnet  crossref  crossref  isi  elib
    22. Yurii V. Zhuchok, “Automorphisms of the endomorphism semigroup of a free abelian diband”, Algebra Discrete Math., 25:2 (2018), 322–332  mathnet
    23. 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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