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.

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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. 
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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/

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