Communications of the
Korean Mathematical Society CKMS

We first give the constructions of (Jordan) higher derivations on a trivial extension algebra and then we provide some sufficient conditions under which a Jordan higher derivation on a trivial extension algebra is a higher derivation. We then proceed to the trivial generalized matrix algebras as a special trivial extension algebra. As an application we characterize the construction of Jordan higher derivations on a triangular algebra. We also provide some illuminating examples of Jordan higher derivations on certain trivial extension algebras which are not higher derivations.

Keywords: higher derivation, Jordan higher derivation, trivial extension algebra, generalized matrix algebra, triangular algebra

MSC numbers: Primary 16W25; Secondary 47B47, 15A78