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Sibirskii Matematicheskii Zhurnal, 2020, Volume 61, Number 1, Pages 194–200
DOI: https://doi.org/10.33048/smzh.2020.61.113 (Mi smj5973) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Equational noethericity of metabelian $r$-groups

N. S. Romanovskiiab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University
Full-text PDF (375 kB) Citations (3)
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DOI: https://doi.org/10.33048/smzh.2020.61.113
Abstract: The author had earlier defined the concept of an $r$-group, generalizing the concept of a rigid (solvable) group. This article proves that every metabelian $r$-group is equationally Noetherian; i.e., each system of equations in finitely many variables with coefficients in the group is equivalent to some finite subsystem.
Keywords: metabelian group, divisible group, equationally Noetherian group.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00100_а
The author was supported by the Russian Foundation for Basic Research (Grant 18-01-00100).
Received: 13.04.2019
Revised: 13.04.2019
Accepted: 24.07.2019
English version:
Siberian Mathematical Journal, 2020, Volume 61, Issue 1, Pages 154–158
DOI: https://doi.org/10.1134/S0037446620010139
Bibliographic databases:
Document Type: Article
UDC: 512.5
MSC: 35R30
Language: Russian
Citation: N. S. Romanovskii, “Equational noethericity of metabelian $r$-groups”, Sibirsk. Mat. Zh., 61:1 (2020), 194–200; Siberian Math. J., 61:1 (2020), 154–158
Citation in format AMSBIB
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\by N.~S.~Romanovskii
\paper Equational noethericity of metabelian $r$-groups
\jour Sibirsk. Mat. Zh.
\yr 2020
\vol 61
\issue 1
\pages 194--200
\mathnet{http://mi.mathnet.ru/smj5973}
\crossref{https://doi.org/10.33048/smzh.2020.61.113}
\transl
\jour Siberian Math. J.
\yr 2020
\vol 61
\issue 1
\pages 154--158
\crossref{https://doi.org/10.1134/S0037446620010139}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000516567300013}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Сибирский математический журнал Siberian Mathematical Journal
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    References:36
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