Multiplicative generalized Lie n-derivations on completely distributive commutative subspace lattice algebras

Abstract

. Let Alg L be a completely distributive commutative subspace lattice algebra and let δ : Alg L → Alg L be a nonlinear map. It is shown that δ is a multiplicative generalized Lie n -derivation on Alg L with an associated multiplicative generalized Lie n -derivation d if and only if δ ( A ) = ψ ( A )+ ξ ( A ) holds for every A ∈ Alg L , where ψ : Alg L → Alg L is an additive generalized derivation and ξ : Alg L → Z ( Alg L ) is a central-valued map vanishing on each ( n − 1 ) -th commutator p n ( A 1 , A 2 , ··· , A n ) .