Romanovskiĭ, N. S.; Shestakov, I. P. Noetherianness of wreath products of abelian Lie algebras with respect to equations of universal enveloping algebra. (Russian, English) Zbl 1164.17010 Algebra Logika 47, No. 4, 475-490 (2008); translation in Algebra Logic 47, No. 4, 269-278 (2008). Summary: It is proved that the 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 rankalso has this property. Cited in 4 Documents MSC: 17B05 Structure theory for Lie algebras and superalgebras 17B01 Identities, free Lie (super)algebras Keywords:Abelian finite-dimensional algebra; Noetherianness; equations of universal enveloping algebra PDFBibTeX XMLCite \textit{N. S. Romanovskiĭ} and \textit{I. P. Shestakov}, Algebra Logika 47, No. 4, 475--490 (2008; Zbl 1164.17010); translation in Algebra Logic 47, No. 4, 269--278 (2008) Full Text: DOI