A characterization of the Kostrikin radical of a Lie algebra
In this paper we study if the Kostrikin radical of a Lie algebra is
the intersection of all its strongly prime ideals, and prove that this result
is true for Lie algebras over fields of characteristic zero, for Lie algebras
arising from associative algebras over rings of scalars with no 2-torsion, for
Artinian Lie algebras over arbitrary rings of scalars, and for some others. In
all these cases, this implies that nondegenerate Lie algebras are subdirect
products of strongly prime Lie algebras, providing a structure theory for Lie
algebras without any restriction on their dimension.
E. García < esther.garcia@urjc.es >
M. Gómez Lozano < magomez@agt.cie.uma.es >