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Sibirskii Matematicheskii Zhurnal, 2024, Volume 65, Number 3, Pages 577–590
DOI: https://doi.org/10.33048/smzh.2024.65.311 (Mi smj7874) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Constructions of quandles over groups and rings

A. A. Simonova, M. V. Neshchadimb, A. N. Borodinc

a Novosibirsk State University
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
c Gorno-Altaisk State University
Full-text PDF (266 kB) Citations (3)
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DOI: https://doi.org/10.33048/smzh.2024.65.311
Abstract: We present the following constructions: extension of a trivial quandle by a group with a nontrivial abelian subgroup, a quandle over a noncommutative group by an arbitrary antiautomorphism, a quandle presenting from a generalized Alexander quandle with the replacement of the automorphism by a central antiautomorphism, and a quandle over an $n$-dimensional module depending on $n(n-1)-1$ parameters with $n\geq 2$ in a commutative unital ring.
Keywords: quandle, Hosszu quandle, trivial quandle, Alexander quandle, generalized Alexander quandle, self-distributivity, distributive, group, automorphism, antiautomorphism, module, ring.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0009
The work was supported by the Fundamental Research Program of the Siberian Branch of the Russian Academy of Sciences (no. I.1.5, Project FWNF–2022-0009).
Received: 15.01.2024
Revised: 19.02.2024
Accepted: 08.04.2024
English version:
Siberian Mathematical Journal, 2024, Volume 65, Issue 3, Pages 627–638
DOI: https://doi.org/10.1134/S003744662403011X
Document Type: Article
UDC: 512.548+515.162.8
MSC: 35R30
Language: Russian
Citation: A. A. Simonov, M. V. Neshchadim, A. N. Borodin, “Constructions of quandles over groups and rings”, Sibirsk. Mat. Zh., 65:3 (2024), 577–590; Siberian Math. J., 65:3 (2024), 627–638
Citation in format AMSBIB
\Bibitem{SimNesBor24}
\by A.~A.~Simonov, M.~V.~Neshchadim, A.~N.~Borodin
\paper Constructions of quandles over groups and rings
\jour Sibirsk. Mat. Zh.
\yr 2024
\vol 65
\issue 3
\pages 577--590
\mathnet{http://mi.mathnet.ru/smj7874}
\transl
\jour Siberian Math. J.
\yr 2024
\vol 65
\issue 3
\pages 627--638
\crossref{https://doi.org/10.1134/S003744662403011X}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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