Certain Pair of Derivations on a Triangular Algebra

Abstract

By using properties of triangular algebra, we prove that if derivations $D$ and $G$ on a triangular algebra $\mathcal{T}$ satisfy certain generalized identities, then both $D$ and $G$ are zero mappings. As a corollary we get that if $D$ and $G$ are cocentralizing on $\mathcal{T}$, then both $D$ and $G$ are zero mappings.