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Fundamentalnaya i Prikladnaya Matematika, 2003, Volume 9, Issue 3, Pages 65–87 (Mi fpm734)  

This article is cited in 16 scientific papers (total in 16 papers)

Algebraic geometry over free metabelian Lie algebras. II. Finite-field case

E. Yu. Daniyarova, I. V. Kazatchkov, V. N. Remeslennikov

Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Science
References:
Abstract: This paper is the second in a series of three, the object of which is to construct an algebraic geometry over the free metabelian Lie algebra $F$. For the universal closure of a free metabelian Lie algebra of finite rank $r\ge2$ over a finite field $k$ we find convenient sets of axioms in two distinct languages: with constants and without them. We give a description of the structure of finitely generated algebras from the universal closure of $F_r$ in both languages mentioned and the structure of irreducible algebraic sets over $F_r $ and respective coordinate algebras. We also prove that the universal theory of free metabelian Lie algebras over a finite field is decidable in both languages.
English version:
Journal of Mathematical Sciences (New York), 2006, Volume 135, Issue 5, Pages 3311–3326
DOI: https://doi.org/10.1007/s10958-006-0160-4
Bibliographic databases:
UDC: 512.554.3
Language: Russian
Citation: E. Yu. Daniyarova, I. V. Kazatchkov, V. N. Remeslennikov, “Algebraic geometry over free metabelian Lie algebras. II. Finite-field case”, Fundam. Prikl. Mat., 9:3 (2003), 65–87; J. Math. Sci., 135:5 (2006), 3311–3326
Citation in format AMSBIB
\Bibitem{DanKazRem03}
\by E.~Yu.~Daniyarova, I.~V.~Kazatchkov, V.~N.~Remeslennikov
\paper Algebraic geometry over free metabelian Lie algebras.~II. Finite-field case
\jour Fundam. Prikl. Mat.
\yr 2003
\vol 9
\issue 3
\pages 65--87
\mathnet{http://mi.mathnet.ru/fpm734}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2094330}
\zmath{https://zbmath.org/?q=an:1072.17005}
\transl
\jour J. Math. Sci.
\yr 2006
\vol 135
\issue 5
\pages 3311--3326
\crossref{https://doi.org/10.1007/s10958-006-0160-4}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33744726179}
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  • https://www.mathnet.ru/eng/fpm/v9/i3/p65
  • This publication is cited in the following 16 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Фундаментальная и прикладная математика
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