For any abelian inner ideal B of a Lie algebra L such that [B, KerB]^n ⊆ B for some natural n, we build a bounded filtration whose first nonzero term is B and the extremes of the induced Z-graded Lie algebra coincide with the subquotient (B, L/KerB). Thanks to this fi ltration, we can prove that when a Lie algebra L is strongly prime and KerB is not a subalgebra of L, then subquotient (B, L=KerB) is a special strongly prime Jordan pair.
