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Sibirsk. Mat. Zh., 2015, Volume 56, Number 5, Pages 1037–1053 (Mi smj2695)  
This article is cited in 6 scientific papers (total in 6 papers)

Dimonoids and bar-units

A. V. Zhuchok

Lugansk Taras Shevchenko National University, Institute of Physics, Mathematics and Information Technologies, Starobilsk, Ukraine

Abstract: A. P. Pozhidaev proved that each dialgebra may be embedded into a dialgebra with a barunit. As is known, a dialgebra is a vector space with two binary operations satisfying the axioms of a dimonoid. It is natural in this situation to pose the problem about the possibility of adjoining bar-units to dimonoids in a given class and the problem of embedding dimonoids into dimonoids with bar-units.
In the present article these problems are solved for some classes of dimonoids. In particular, we show that it is impossible to adjoin a set of bar-units to a free dimonoid. Also, we solve the problem of embedding an arbitrary dimonoid into a dimonoid with bar-units.

Keywords: dimonoid, bar-unit, adjoining a set of bar-units, free dimonoid, free rectangular dimonoid, free commutative dimonoid, free $n$-(di)nilpotent dimonoid, semigroup, automorphism group.

DOI: https://doi.org/10.17377/smzh.2015.56.505

Full text: PDF file (338 kB)
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English version:
Siberian Mathematical Journal, 2015, 56:5, 827–840

Bibliographic databases:

UDC: 512.57+512.579
Received: 25.08.2014
Revised: 25.05.2015

Citation: A. V. Zhuchok, “Dimonoids and bar-units”, Sibirsk. Mat. Zh., 56:5 (2015), 1037–1053; Siberian Math. J., 56:5 (2015), 827–840

Citation in format AMSBIB
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\by A.~V.~Zhuchok
\paper Dimonoids and bar-units
\jour Sibirsk. Mat. Zh.
\yr 2015
\vol 56
\issue 5
\pages 1037--1053
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\crossref{https://doi.org/10.17377/smzh.2015.56.505}
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\transl
\jour Siberian Math. J.
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\vol 56
\issue 5
\pages 827--840
\crossref{https://doi.org/10.1134/S0037446615050055}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Fausto Ongay, Raúl Velásquez, Luis Alberto Wills-Toro, “Normal subdigroups and the isomorphism theorems for digroups”, Algebra Discrete Math., 22:2 (2016), 262–283  mathnet  mathscinet
    2. Anatolii V. Zhuchok, Milan Demko, “Free $n$-dinilpotent doppelsemigroups”, Algebra Discrete Math., 22:2 (2016), 304–316  mathnet  mathscinet
    3. A. V. Zhuchok, A. B. Gorbatkov, “On the structure of dimonoids”, Semigr. Forum, 94:2 (2017), 194–203  crossref  mathscinet  zmath  isi  scopus
    4. A. V. Zhuchok, “Structure of relatively free dimonoids”, Commun. Algebr., 45:4 (2017), 1639–1656  crossref  mathscinet  zmath  isi  scopus
    5. Anatolii V. Zhuchok, Kolja Knauer, “Abelian doppelsemigroups”, Algebra Discrete Math., 26:2 (2018), 290–304  mathnet
    6. Yuri Movsisyan, “On functional equations and distributive second order formulae with specialized quantifiers”, Algebra Discrete Math., 25:2 (2018), 269–285  mathnet
    		• Сибирский математический журнал Siberian Mathematical Journal
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