Some Upper Bounds for the Dimension of the c-Nilpotent Multiplier of a Pair of Lie Algebras

The notion of the Schur multiplier of a Lie algebra was introduced by Batten in 1996. Recently, the first author introduced the concept of the cnilpotent multiplier of a pair of Lie algebras and gave some exact sequences for the -nilpotent multiplier of a pair of Lie algebras. The purpose of this paper is to derive some inequalities for dimension of the -nilpotent multiplier of a pair of Lie algebras.