3-Lie algebras with an ideal N

We define the hypo-nilpotent ideal in n-Lie algebras and obtain all solvable 3-Lie algebras with an m-dimensional simplest filiform 3-Lie algebra as a maximal hypo-nilpotent ideal. We prove that the dimension of such solvable 3-Lie algebras is at most m+2, and there is no solvable 3-Lie algebra with the simplest filiform 3-Lie algebra as the nilradical.