A Note on Jordan Derivations of Trivial Generalized Matrix Algebras

Abstract

Abstract. H. R. Ebrahimi Vishki et al. conjectured in [1], that if every Jordan higher derivation on a trivial generalized matrix algebra G = (A, M, N, B) is a higher derivation, then either M = 0 or N = 0. In this note, we will give a class of counter examples.