Characterization of Generalized Jordan Higher Derivations on Triangular rings

Abstract

Let $\mathcal{A}$ and $\mathcal{B}$ be unital rings and $\mathcal{M}$ be a $(\mathcal{A},\mathcal{B})$-bimodule, which is faithful as a left $\mathcal{A}$-module and also as a right $\mathcal{B}$-module. Let $\mathcal{U}=\mathrm{Tri}(\mathcal{A},\mathcal{M},\mathcal{B})$ be the associated triangular ring. It is shown that every additive generalized Jordan (triple) higher derivation on $\mathcal{U}$ is a generalized higher derivation.

12 pages