Higher derivations of triangular algebras and its generalizations

Abstract

Let R be a commutative ring with identity, A and B be unital algebras over R and M be a unital (it A,it B)-bimodule. Let T = A M 0 B be the triangular algebra consisting of A, it Band M. Motivated by the work of Cheung [14] we mainly consider the question whether every higher derivation on a triangular algebra is an inner higher derivation. We also give some characterizations on (generalized-)Jordan (triple-)higher derivations of triangular algebras.