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Algebra Logika, 2013, Volume 52, Number 3, Pages 386–391 (Mi al593)  

This article is cited in 2 scientific papers (total in 2 papers)

Irreducibility of an affine space in algebraic geometry over a group

N. S. Romanovskiiab

a Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia
b Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

Abstract: We prove a theorem which states that if $G$ is an equationally Noetherian group that is locally approximated by finite $p$-groups for each prime $p$ then an affine space $G^n$ in a respective Zariski topology is irreducible for any $n$. The hypothesis of the theorem is satisfied by free groups, free soluble groups, free nilpotent groups, finitely generated torsion-free nilpotent groups, and rigid soluble groups. Also we introduce corrections to a lemma on valuations, which has been used in some of the author's previous works.

Keywords: Zariski topology, equationally Noetherian group, affine space, algebraic geometry over group.

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English version:
Algebra and Logic, 2013, 52:3, 262–265

Bibliographic databases:

UDC: 512.5
Received: 20.05.2013

Citation: N. S. Romanovskii, “Irreducibility of an affine space in algebraic geometry over a group”, Algebra Logika, 52:3 (2013), 386–391; Algebra and Logic, 52:3 (2013), 262–265

Citation in format AMSBIB
\Bibitem{Rom13}
\by N.~S.~Romanovskii
\paper Irreducibility of an affine space in algebraic geometry over a~group
\jour Algebra Logika
\yr 2013
\vol 52
\issue 3
\pages 386--391
\mathnet{http://mi.mathnet.ru/al593}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3137131}
\transl
\jour Algebra and Logic
\yr 2013
\vol 52
\issue 3
\pages 262--265
\crossref{https://doi.org/10.1007/s10469-013-9239-4}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000325007400007}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. A. Roman'kov, N. G. Khisamiev, “Existentially closed subgroups of free nilpotent groups”, Algebra and Logic, 53:1 (2014), 29–38  mathnet  crossref  mathscinet  isi
    2. E. Yu. Daniyarova, A. G. Myasnikov, V. N. Remeslennikov, “Algebraic geometry over algebraic structures. VI. Geometric equivalence”, Algebra and Logic, 56:4 (2017), 281–294  mathnet  crossref  crossref  isi
  • Алгебра и логика Algebra and Logic
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