The aim of this paper is to show a close relationship between the factoralgebras by the terms of the upper central series ζ n (L) of a Leibniz algebra L and the terms of its lower central series γ n (L). Specifically we show that finiteness of codimension of some ζ k (L) implies finiteness of dimension of γ k+1 (L) and give explicit bounds for this dimension. We also improve this in the case k = 1, which corresponds to the center and commutator subalgebra of the algebra, respectively. These results are analogous to the results that have been obtained for groups and Lie algebras.

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