Geodesic
Noetherianness of wreath products of Abelian Lie algebras with respect to equations of universal enveloping algebra
Algebra i logika, Tome 47 (2008) no. 4, pp. 475-490 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

It is proved that a wreath product of two Abelian finite-dimensional Lie algebras over a field of characteristic zero is Noetherian w.r.t. equations of a universal enveloping algebra. This implies that an index 2 soluble free Lie algebra of finite rank, too, has this property.
Keywords: Abelian finite-dimensional algebra, Noetherianness w.r.t. equations of universal enveloping algebra. 
@article{AL_2008_47_4_a4,
     author = {N. S. Romanovskii and I. P. Shestakov},
     title = {Noetherianness of wreath products of {Abelian} {Lie} algebras with respect to equations of universal enveloping algebra},
     journal = {Algebra i logika},
     pages = {475--490},
     year = {2008},
     volume = {47},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2008_47_4_a4/}
}
TY  - JOUR
AU  - N. S. Romanovskii
AU  - I. P. Shestakov
TI  - Noetherianness of wreath products of Abelian Lie algebras with respect to equations of universal enveloping algebra
JO  - Algebra i logika
PY  - 2008
SP  - 475
EP  - 490
VL  - 47
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/AL_2008_47_4_a4/
LA  - ru
ID  - AL_2008_47_4_a4
ER  - 
%0 Journal Article
%A N. S. Romanovskii
%A I. P. Shestakov
%T Noetherianness of wreath products of Abelian Lie algebras with respect to equations of universal enveloping algebra
%J Algebra i logika
%D 2008
%P 475-490
%V 47
%N 4
%U http://geodesic.mathdoc.fr/item/AL_2008_47_4_a4/
%G ru
%F AL_2008_47_4_a4
N. S. Romanovskii; I. P. Shestakov. Noetherianness of wreath products of Abelian Lie algebras with respect to equations of universal enveloping algebra. Algebra i logika, Tome 47 (2008) no. 4, pp. 475-490. http://geodesic.mathdoc.fr/item/AL_2008_47_4_a4/

[1] B. Plotkin, “Varieties of algebras and algebraic varieties”, Isr. J. Math., 96, Pt. B (1996), 511–522 | DOI | MR | Zbl

[2] G. Baumslag, A. Myasnikov, V. Remeslennikov, “Algebraic geometry over groups. I: Algebraic sets and ideal theory”, J. Algebra, 219, no. 1, 16–79 | MR | Zbl

[3] A. Myasnikov, V. Remeslennikov, “Algebraic geometry over groups. II. Logical foundations”, J. Algebra, 234:1 (2000), 225–276 | DOI | MR | Zbl

[4] E. Yu. Daniyarova, Elementy algebraicheskoi geometrii nad algebrami Li, preprint No 131, In-t matem. SO RAN, Novosibirsk, 2004

[5] Ch. K. Gupta, N. S. Romanovskii, “Neterovost po uravneniyam nekotorykh razreshimykh grupp”, Algebra i logika, 46:1 (2007), 46–59 | MR

[6] A. L. Shmelkin, “Spleteniya algebr Li i ikh primenenie v teorii grupp”, Tr. mosk. matem. ob-va, 29, 1973, 247–260