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Algebra and Discrete Mathematics, 2021, Volume 31, Issue 1, Pages 152–166
DOI: https://doi.org/10.12958/adm1732
(Mi adm793)
 

This article is cited in 4 scientific papers (total in 4 papers)

RESEARCH ARTICLE

Structure of relatively free trioids

A. V. Zhuchok

Department of Algebra and System Analysis, Luhansk Taras Shevchenko National University, Gogol Square, 1, Starobilsk 92703, Ukraine
Full-text PDF (351 kB) Citations (4)
References:
Abstract: Loday and Ronco introduced the notions of a trioid and a trialgebra, and constructed the free trioid of rank $1$ and the free trialgebra. This paper is a survey of recent developments in the study of free objects in the varieties of trioids and trialgebras. We present the constructions of the free trialgebra and the free trioid, the free commutative trioid, the free $n$-nilpotent trioid, the free left (right) $n$-trinilpotent trioid, and the free rectangular trioid. Some of these results can be applied to constructing relatively free trialgebras.
Keywords: trioid, trialgebra, free trioid, free trialgebra, relatively free trioid, semigroup.
Funding agency Grant number
National Research Foundation of Ukraine 2020.02/0066
The author is supported by the National Research Foundation of Ukraine (grant no. 2020.02/0066).
Received: 30.11.2020
Document Type: Article
Language: English
Citation: A. V. Zhuchok, “Structure of relatively free trioids”, Algebra Discrete Math., 31:1 (2021), 152–166
Citation in format AMSBIB
\Bibitem{Zhu21}
\by A.~V.~Zhuchok
\paper Structure of relatively free trioids
\jour Algebra Discrete Math.
\yr 2021
\vol 31
\issue 1
\pages 152--166
\mathnet{http://mi.mathnet.ru/adm793}
\crossref{https://doi.org/10.12958/adm1732}
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  • https://www.mathnet.ru/eng/adm/v31/i1/p152
  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Algebra and Discrete Mathematics
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