Generalized higher (U,M)-derivations in prime Γ-Rings.

Let M be a 2-torsion free prime Γ-ring satisfying the condition a α b ß c=a ß b α c,∀a,b,c∈M and α,ß∈Γ, U be an admissible Lie ideal of M and F=(f i ) i∈N be a generalized higher (U,M)-derivation of M with an associated higher (U,M)-derivation D=(d i ) i∈N of M. Then for all n∈N we prove that [Formula: see text]. Mathematics Subject Classification (2010): 13N15; 16W10; 17C50.