On the lower weakly solvable $l$-radical of lattice ordered Lie algebras

The concept of the lower weakly solvable radical of Lie algebras is important in the study of Lie algebras. The purpose of this paper is to investigate the generalization of this concept to lattice ordered Lie algebras over partially ordered fields. Some results concerning properties of the lower weakly solvable $l$-radical of lattice ordered Lie algebras are obtained. Necessary and sufficient conditions for the $l$-prime radical of a Lie $l$-algebra to be equal to the lower weakly solvable $l$-radical of the Lie $l$-algebra are presented.