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Fundamentalnaya i Prikladnaya Matematika, 2003, Volume 9, Issue 3, Pages 65–87
(Mi fpm734)
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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
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.
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
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https://www.mathnet.ru/eng/fpm734 https://www.mathnet.ru/eng/fpm/v9/i3/p65
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Abstract page: | 403 | Full-text PDF : | 131 | References: | 69 | First page: | 1 |
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