فهرست نشریات علمی دسترسی آزاد ایران

In this article, we study Jordan higher derivations on unital algebras with non-trivial idempotent. We extend some previous results on Jordan derivations of such algebras to Jordan higher derivations and show that, under mild conditions, every Jordan higher derivation on a unital algebra with a non-trivial idempotent is a higher derivation. We apply this result to  several classes of matrix algebras, including the triangular algebra $\mathrm{Tri}(A, X, B)$, the algebra of upper triangular matrices $T_n(\cR)$, and the nest algebra $T(\cN)$. This allows us to extend previous results on Jordan derivations to Jordan higher derivations for these algebras.