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Algebra Discrete Math., 2013, Volume 16, Issue 2, Pages 299–310 (Mi adm454)  

This article is cited in 8 scientific papers (total in 8 papers)

RESEARCH ARTICLE

Free $n$-nilpotent dimonoids

A. V. Zhuchok

Department of Mathematical Analysis and Algebra, Luhansk Taras Shevchenko National University, Oboronna str., 2, Luhansk, 91011, Ukraine

Abstract: We construct a free $n$-nilpotent dimonoid and describe its structure. We also characterize the least $n$-nilpotent congruence on a free dimonoid, construct a new class of dimonoids with zero and give examples of nilpotent dimonoids of nilpotency index $2$.

Keywords: $n$-nilpotent dimonoid, free $n$-nilpotent dimonoid, $0$-diband of subdimonoids, dimonoid, semigroup.

Full text: PDF file (212 kB)
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Bibliographic databases:
MSC: 08B20, 20M10, 20M50, 17A30, 17A32
Received: 02.07.2013
Revised: 27.08.2013
Language:

Citation: A. V. Zhuchok, “Free $n$-nilpotent dimonoids”, Algebra Discrete Math., 16:2 (2013), 299–310

Citation in format AMSBIB
\Bibitem{Zhu13}
\by A.~V.~Zhuchok
\paper Free $n$-nilpotent dimonoids
\jour Algebra Discrete Math.
\yr 2013
\vol 16
\issue 2
\pages 299--310
\mathnet{http://mi.mathnet.ru/adm454}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3186091}


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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. Yuliia V. Zhuchok, “On one class of algebras”, Algebra Discrete Math., 18:2 (2014), 306–320  mathnet  mathscinet
    2. A. V. Zhuchok, “Dimonoids and bar-units”, Siberian Math. J., 56:5 (2015), 827–840  mathnet  crossref  crossref  isi  elib  elib
    3. A. Zhuchok, Yu. Zhuchok, “Free left $n$-dinilpotent dimonoids”, Semigr. Forum, 93:1 (2016), 161–179  crossref  mathscinet  zmath  isi  scopus
    4. Anatolii V. Zhuchok, Milan Demko, “Free $n$-dinilpotent doppelsemigroups”, Algebra Discrete Math., 22:2 (2016), 304–316  mathnet  mathscinet
    5. A. V. Zhuchok, “Structure of relatively free dimonoids”, Commun. Algebr., 45:4 (2017), 1639–1656  crossref  mathscinet  zmath  isi  scopus
    6. A. V. Zhuchok, “Free products of doppelsemigroups”, Algebr. Universalis, 77:3 (2017), 361–374  crossref  mathscinet  zmath  isi  scopus
    7. A. V. Zhuchok, “Free $n$-Tuple Semigroups”, Math. Notes, 103:5 (2018), 737–744  mathnet  crossref  crossref  isi  elib
    8. A. V. Zhuchok, “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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