A Note on a Result of Kostrikin
2009; Taylor & Francis; Volume: 37; Issue: 7 Linguagem: Inglês
10.1080/00927870802255683
ISSN1532-4125
AutoresEsther Garcı́a, Miguel Gómez Lozano,
Tópico(s)Rings, Modules, and Algebras
ResumoAbstract Let L be a Lie algebra over a ring of scalars in which 2, 3,…, r are invertible, and let x be an ad-nilpotent element of index n with . We prove that is an abelian inner ideal of L. In particular, for every a ∈ L, is ad-nilpotent of index at most 3, which extends a result of Kostrikin [Citation2, Lemma 1.1, p. 31]. Key Words: Ad-nilpotent elementInner idealLie algebra2000 Mathematics Subject Classification: 17B30 ACKNOWLEDGEMENTS The first author was partially supported by the MEC and Fondos FEDER, MTM2007-62390, by the Plan de Investigación del Principado de Asturias FICYT-IB05-017, y Programa de Creación y Consolidación de Grupos de Investigación URCJ-CM-2006-CET-0585. The second author was partially supported by the MEC and Fondos FEDER, MTM2007-61978, by the Plan de Investigación del Principado de Asturias FICYT-IB05-017, and by the Junta de Andalucía FQM264. Notes Communicated by A. Elduque.
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