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Algebra Discrete Math., 2016, Volume 22, Issue 2, Pages 304–316 (Mi adm590)  

This article is cited in 6 scientific papers (total in 6 papers)

RESEARCH ARTICLE

Free $n$-dinilpotent doppelsemigroups

Anatolii V. Zhuchoka, Milan Demkob

a Department of Algebra and System Analysis, Luhansk Taras Shevchenko National University, Gogol square, 1, Starobilsk, 92703, Ukraine
b Department of Physics, Mathematics and Techniques, University of Presov, Slovakia, 17. novembra 1, Presov, 08116, Slovakia

Abstract: A doppelalgebra is an algebra defined on a vector space with two binary linear associative operations. Doppelalgebras play a prominent role in algebraic $K$-theory. In this paper we consider doppelsemigroups, that is, sets with two binary associative operations satisfying the axioms of a doppelalgebra. We construct a free $n$-dinilpotent doppelsemigroup and study separately free $n$-dinilpotent doppelsemigroups of rank $1$. Moreover, we characterize the least $n$-dinilpotent congruence on a free doppelsemigroup, establish that the semigroups of the free $n$-dinilpotent doppelsemigroup are isomorphic and the automorphism group of the free $n$-dinilpotent doppelsemigroup is isomorphic to the symmetric group. We also give different examples of doppelsemigroups and prove that a system of axioms of a doppelsemigroup is independent.

Keywords: doppelalgebra, interassociativity, doppelsemigroup, free $n$-dinilpotent doppelsemigroup, free doppelsemigroup, semigroup, congruence.

Funding Agency Grant Number
Ministerstvo Školstva, Vedy, Výskumu a Športu Slovenskej Republiky 1/0063/14
The second author acknowledges the support of the Slovak VEGA Grant No. 1/0063/14.


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Bibliographic databases:
MSC: 08B20, 20M10, 20M50, 17A30
Received: 03.10.2016
Revised: 30.11.2016
Language:

Citation: Anatolii V. Zhuchok, Milan Demko, “Free $n$-dinilpotent doppelsemigroups”, Algebra Discrete Math., 22:2 (2016), 304–316

Citation in format AMSBIB
\Bibitem{ZhuDem16}
\by Anatolii~V.~Zhuchok, Milan~Demko
\paper Free $n$-dinilpotent doppelsemigroups
\jour Algebra Discrete Math.
\yr 2016
\vol 22
\issue 2
\pages 304--316
\mathnet{http://mi.mathnet.ru/adm590}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3593127}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000392709600011}


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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. Yu. M. Movsisyan, “Hyperidentities and related concepts, I”, Armen. J. Math., 9:2 (2017), 146–222  mathscinet  zmath  isi
    2. A. V. Zhuchok, “Free left $n$-dinilpotent doppelsemigroups”, Commun. Algebr., 45:11 (2017), 4960–4970  crossref  mathscinet  zmath  isi  scopus
    3. A. V. Zhuchok, K. Knauer, “Abelian doppelsemigroups”, Algebra Discret. Math., 26:2 (2018), 290–304  mathnet  mathscinet  zmath  isi
    4. Yu. M. Movsisyan, “On functional equations and distributive second order formulae with specialized quantifiers”, Algebra Discret. Math., 25:2 (2018), 269–285  mathnet  mathscinet  zmath  isi
    5. Yu. M. Movsisyan, “Hyperidentities and related concepts, II”, Armen. J. Math., 10:4 (2018), 1–85  mathscinet  isi
    6. 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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