Bounds in Lie algebras with trivial subalgebra

In 1904, Schur proved that if the center of a group G has finite index, then the drived subgroup, G′ is also finite. The Lie algebra analogue of Schur’s theorem is well-known. In 1994, Moneyhun showed that if L is a Lie algebra such that dim (L/Z(L)) = n, then dim (L^2) ≤ n(n−1)/2.The first author and F. Saeedi investigated the converse of Moneyhun’s theorem under some conditions. In this paper, we will extend their results