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Algebra i logika, 2000, Volume 39, Number 3, Pages 249–272 (Mi al276)  

This article is cited in 11 scientific papers (total in 11 papers)

$G$-identities and $G$-varieties

M. G. Amaglobeli, V. N. Remeslennikov
Abstract: G. Baumslag, A. Myasnikov and Remeslennikov [J. Algebra 219 (1999), no. 1, 16–79; MR1707663 (2000j:14003)] presented the fundamentals of algebraic geometry over a fixed group $G$; in particular, they introduced the concept of a category of $G$-groups. For groups in this category, one can also define the concepts of $G$-identity and $G$-variety. We present the fundamentals of the theory of varieties in the category of $G$-groups, of which the most essential is the concept of the group $V_{n,\mathrm{red}}(G)$ of reduced $G$-identities of rank $n$, which is important for the computation of the coordinate groups for algebraic sets over $G$. We prove that $V_{n,\mathrm{red}}(G)=1$ for all natural numbers $n$ if $G$ is a group that is close to a free or relatively free group for some variety of nilpotent groups of rank not less than the nilpotency class of $G$.
Received: 17.11.1999
English version:
Algebra and Logic, 2000, Volume 39, Issue 3, Pages 141–154
DOI: https://doi.org/10.1007/BF02681758
Bibliographic databases:
UDC: 512.54
Language: Russian
Citation: M. G. Amaglobeli, V. N. Remeslennikov, “$G$-identities and $G$-varieties”, Algebra Logika, 39:3 (2000), 249–272; Algebra and Logic, 39:3 (2000), 141–154
Citation in format AMSBIB
\Bibitem{AmaRem00}
\by M.~G.~Amaglobeli, V.~N.~Remeslennikov
\paper $G$-identities and $G$-varieties
\jour Algebra Logika
\yr 2000
\vol 39
\issue 3
\pages 249--272
\mathnet{http://mi.mathnet.ru/al276}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1782323}
\zmath{https://zbmath.org/?q=an:0966.20014}
\transl
\jour Algebra and Logic
\yr 2000
\vol 39
\issue 3
\pages 141--154
\crossref{https://doi.org/10.1007/BF02681758}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33846633925}
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  • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Алгебра и логика Algebra and Logic
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