(33). Characterizations of the kostrikin radical of a Lie algebra.
Autores: E. García y M. Gómez Lozano.
Revista:: Journal of Algebra, 346 (1), p.266-283, Nov 2011 (JCR: 127 de 289 Factor de impacto: 0.613)
Abstract: In this paper we investigate characterizations of the Kostrikin radical of a Lie algebra in terms of strongly prime ideals and in terms of m-sequences. We solve these questions for Lie algebras arising from associative algebras, for Artinian Lie algebras, and for Lie algebras over fields of characteristic zero in which every nonzero ideal contains nonzero ad-nilpotent elements that do not belong to the Kostrikin radical. Moreover, we show that the intersection of all strongly prime ideals of a Lie algebra over a field of characteristic zero is a radical in the sense Amitsur-Kurosh.
socle, and satisfies the descending chain condition on principal inner ideals. Furthermore, we give a structure theory for nondegenerate Lie algebras containing abelian minimal inner