An elemental characterization of strong primeness in Lie algebras

Abstract: In this paper we prove that a Lie algebra L is strongly prime if and only if for every nonzero elements . As a consequence, we give an elementary proof, without the classification theorem of strongly prime Jordan algebras, of the fact that a linear Jordan algebra or Jordan pair T is strongly prime if and only if for every . Moreover, we prove that the Jordan algebras at nonzero Jordan elements of strongly prime Lie algebras are strongly prime. [Copyright &y& Elsevier]