NONLINEAR JORDAN HIGHER DERIVATIONS ON TRIANGULAR RINGS

Let T be a triangular ring. We say that a family of maps delta = {delta(n), delta(n) : T -> T, n is an element of N} is a Jordan higher derivable map (without assumption of additivity or continuity) if delta(n)(AB + BA) = Sigma(i+j=n)[delta(i)(A)delta(j)(B)+delta(j)(B)delta(i)(A)] for all A, B is an element of T. In this paper, we show that every Jordan higher derivable map on a triangular ring is a higher derivation. As its application, we get that every Jordan higher derivable map on an irreducible CDCSL algebra or a nest algebra is a higher derivation, and new characterizations of higher derivations on these algebras are obtained.