Subideals Of 3-Lie Algebras

We know that subideals are the fundation of the struture of 3-Lie algebras. In this paper the properties of subideals of 3-Lie algebras are studied. First, results that subide-als of solvble (nilpotent) 3-Lie algebras are still solvable (nilpotent) and the subalgebra generated by two permuttable n-step solvable subideals is still solvable are proved, and a sufficient condition which the sum of permutable subideals is also a subideal is provided. At the last of the paper, relations between the ordered subalgebra pairs and subideals are investigated.The orgniaztion of the paper is as follows:The section I introduces some defi-nitions. The section 2 studies solvability and nilpotency of subideals. The section 3 discusses permutability of subideals. The section 4 researches relations between the ordered subalgebra pairs and subideals.