Geodesic
Axioms of metabelian Lie Q-algebras and U-algebras
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 9 (2012), pp. 266-284.

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This is the third paper in the series of three, which are in the series of papers, the aim of which is to construct algebraic geometry over metabelian Lie algebras. We give the recursive set of universal formulas, axiomatizing universal class of all matabelian Lie U-algebras, and the recursive set of quasiidentities, axiomatizing quasivariety of all matabelian Lie Q-algebras. We have come to the characterization of finite generated objects from these universal classes. We show connections between such algebras and diophantine projective varieties over a field.
Keywords: matabelian Lie algebra over a field, Q-algebra, U-algebra, U-primary algebra, Q-semiprimary algebra, quasivariety, universal closure, diophantine projective variety over a field. 
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E. Yu. Daniyarova. Axioms of metabelian Lie Q-algebras and U-algebras. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 9 (2012), pp. 266-284. http://geodesic.mathdoc.fr/item/SEMR_2012_9_a3/

[1] E. Yu. Daniyarova, “Metabelevy U-algebry Li”, Sibirskie elektronnye matematicheskie izvestiya, 5 (2008), 355–382 http://semr.math.nsc.ru/v5/p355-382.pdf | MR

[2] E. Yu. Daniyarova, “Metabelevy Q-algebry Li”, Sibirskie elektronnye matematicheskie izvestiya, 6 (2009), 26–48 http://semr.math.nsc.ru/v6/p26-48.pdf | MR

[3] A. I. Maltsev, Algebraicheskie sistemy, Nauka, Moskva, 1970

[4] V. A. Gorbunov, Algebraicheskaya teoriya kvazimnogoobrazii, Nauchnaya kniga, Novosibirsk, 1999

[5] Spravochnaya kniga po matematicheskoi logike. Chast 1. Teoriya modelei, Nauka, Moskva, 1982

[6] E. Yu. Daniyarova, “Osnovy algebraicheskoi geometrii nad algebrami Li”, Vestnik Omskogo universiteta, Kombinatornye metody algebry i slozhnost vychislenii, 2007, 8–39

[7] E. Yu. Daniyarova, I. V. Kazachkov, V. N. Remeslennikov, “Algebraicheskaya geometriya nad svobodnoi metabelevoi algebroi Li I: U-algebry i universalnye klassy”, Fundam. i prikl. mat., 9:3 (2003), 37–63 http://mech.math.msu.su/~fpm/rus/k03/k033/k03304h.htm | Zbl

[8] E. Yu. Daniyarova, I. V. Kazachkov, V. N. Remeslennikov, “Algebraicheskaya geometriya nad svobodnoi metabelevoi algebroi Li II: Sluchai konechnogo polya”, Fundam. i prikl. mat., 9:3 (2003), 65–87 http://mech.math.msu.su/~fpm/rus/k03/k033/k03305h.htm | Zbl

[9] E. Yu. Daniyarova, “Q-idealy v koltsakh mnogochlenov i Q-moduli nad koltsami mnogochlenov”, Sibirskie elektronnye matematicheskie izvestiya, 4 (2007), 64–84 http://semr.math.nsc.ru/v4/p64-84.pdf | MR

[10] E. Yu. Daniyarova, Algebraicheskaya geometriya nad svobodnoi metabelevoi algebroi Li III: Q-algebry i koordinatnye algebry algebraicheskikh mnozhestv, Preprint, Izd-vo OmGU, Omsk, 2005, 130 pp.