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Sibirskii Matematicheskii Zhurnal, 2022, Volume 63, Number 2, Pages 241–251
DOI: https://doi.org/10.33048/smzh.2022.63.201 (Mi smj7655) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Identities and quasi-identities of pointed algebras

A. O. Basheyevaa, M. Mustafab, A. M. Nurakunovc

a Eurasian National University named after L.N. Gumilyov, Nur-Sultan
b Nazarbayev University Research and Innovation System
c Institute of Mathematics of the National Academy of Sciences of the Kyrgyz Republic
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DOI: https://doi.org/10.33048/smzh.2022.63.201
Abstract: Each pointed enrichment of an algebra can be regarded as the same algebra with an additional finite set of constant operations. An algebra is pointed whenever it is a pointed enrichment of some algebra. We show that each pointed enrichment of a finite algebra in a finitely axiomatizable residually very finite variety admits a finite basis of identities. We also prove that every pointed enrichment of a finite algebra in a directly representable quasivariety admits a finite basis of quasi-identities. We give some applications of these results and examples.
Keywords: variety, quasivariety, identity, quasi-identity, finite axiomatizability, pointed algebra.
Funding agency Grant number
Nazarbayev University FDCRG 021220FD3851
The work was supported by Nazarbayev University FDCRG Grant no.В 021220FD3851.
Received: 24.02.2021
Revised: 14.04.2021
Accepted: 11.06.2021
English version:
Siberian Mathematical Journal, 2022, Volume 63, Issue 2, Pages 197–205
DOI: https://doi.org/10.1134/S003744662202001X
Bibliographic databases:
Document Type: Article
UDC: 512.57
MSC: 35R30
Language: Russian
Citation: A. O. Basheyeva, M. Mustafa, A. M. Nurakunov, “Identities and quasi-identities of pointed algebras”, Sibirsk. Mat. Zh., 63:2 (2022), 241–251; Siberian Math. J., 63:2 (2022), 197–205
Citation in format AMSBIB
\Bibitem{BasMusNur22}
\by A.~O.~Basheyeva, M.~Mustafa, A.~M.~Nurakunov
\paper Identities and quasi-identities of pointed algebras
\jour Sibirsk. Mat. Zh.
\yr 2022
\vol 63
\issue 2
\pages 241--251
\mathnet{http://mi.mathnet.ru/smj7655}
\crossref{https://doi.org/10.33048/smzh.2022.63.201}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4440279}
\transl
\jour Siberian Math. J.
\yr 2022
\vol 63
\issue 2
\pages 197--205
\crossref{https://doi.org/10.1134/S003744662202001X}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Сибирский математический журнал Siberian Mathematical Journal
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