Algebraic geometry over free metabelian Lie algebras.~II. Finite-field case
Fundamentalʹnaâ i prikladnaâ matematika, Tome 9 (2003) no. 3, pp. 65-87
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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.
@article{FPM_2003_9_3_a4,
author = {E. Yu. Daniyarova and I. V. Kazatchkov and V. N. Remeslennikov},
title = {Algebraic geometry over free metabelian {Lie} {algebras.~II.} {Finite-field} case},
journal = {Fundamentalʹna\^a i prikladna\^a matematika},
pages = {65--87},
publisher = {mathdoc},
volume = {9},
number = {3},
year = {2003},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_2003_9_3_a4/}
}
TY - JOUR AU - E. Yu. Daniyarova AU - I. V. Kazatchkov AU - V. N. Remeslennikov TI - Algebraic geometry over free metabelian Lie algebras.~II. Finite-field case JO - Fundamentalʹnaâ i prikladnaâ matematika PY - 2003 SP - 65 EP - 87 VL - 9 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/FPM_2003_9_3_a4/ LA - ru ID - FPM_2003_9_3_a4 ER -
%0 Journal Article %A E. Yu. Daniyarova %A I. V. Kazatchkov %A V. N. Remeslennikov %T Algebraic geometry over free metabelian Lie algebras.~II. Finite-field case %J Fundamentalʹnaâ i prikladnaâ matematika %D 2003 %P 65-87 %V 9 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/FPM_2003_9_3_a4/ %G ru %F FPM_2003_9_3_a4
E. Yu. Daniyarova; I. V. Kazatchkov; V. N. Remeslennikov. Algebraic geometry over free metabelian Lie algebras.~II. Finite-field case. Fundamentalʹnaâ i prikladnaâ matematika, Tome 9 (2003) no. 3, pp. 65-87. http://geodesic.mathdoc.fr/item/FPM_2003_9_3_a4/