In this article, we give the structure of all covers of n -Lie algebras with finite dimensional Schur multipliers, which generalizes an earlier work of Salemkar et.al.Also, For an n -Lie algebra A of dimension d , we find the upper bound dim M(A) d n , where M(A) denotes the Schur multiplier of A and that the equality holds if and only if A is abelian.Finally, we give a formula for the dimension of the Schur multiplier of the direct sum of two n -Lie algebras.
Darabi et al. (Sun,) studied this question.