Characterizations of generalized Lie n-higher derivations on certain triangular algebras

The aim of this paper was to provide a characterization of nonlinear generalized Lie nhigher derivations for a certain class of triangular algebras. It was shown that, under some mild conditions, each component Gr of a nonlinear generalized Lie n-higher derivation {G r } rEN of the triangular algebra U could be expressed as the sum of an additive generalized higher derivation and a nonlinear mapping vanishing on all (n - 1)-th commutators on U .