证明了中心为零的Jordan李代数能够分解成不可分解理想的直和,这种分解在不计理想次序的前提下是唯一的,并运用Jordan李代数的Engel定理,得到了Jordan李代数的Frattini子代数的若干性质和幂零Jordan李代数的几个判定方法.
This paper will prove that a Jordan Lie algebra satisfying C(J)={0} can be decomposed into direct sum of indecomposable ideals and this decomposition is unique up to the order of the ideals,give its Frattini theory and obtain some sufficient and necesary conditions of nilpotent Jordan Lie algebras using Engel's theorem of a Jordan Lie algebra.