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 $F$.
For the universal closure of a free metabelian Lie algebra of finite
rank $r$³ 2 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.

Location: http://mech.math.msu.su/~fpm/eng/k03/k033/k03305h.htm.

Last modified: January 24, 2005.