Some inequalities for the dimension of the c-nilpotent multiplier of Lie algebras

In this article, we introduce the concept of the c-nilpotent multiplier M(c)(L) of a (finite-dimensional) Lie algebra L, and obtain some inequalities and certain bounds for the dimension of M(c)(L). Also, some inequalities for the dimensions of the derived subalgebra and Schur multiplier of finite-dimensional nilpotent Lie algebras will be given.