FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2003, VOLUME 9, NUMBER 3, PAGES 65-87
Algebraic geometry over free metabelian Lie algebras. II.
Finite-field case
E. Yu. Daniyarova
I. V. Kazatchkov
V. N. Remeslennikov
Abstract
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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 .
For the universal closure of a free metabelian Lie algebra of finite
rank ³ 2 over a finite
field 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 r in both
languages mentioned and the structure of irreducible algebraic sets
over 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.
Location: http://mech.math.msu.su/~fpm/eng/k03/k033/k03305h.htm.
Last modified: January 24, 2005.