A Note of Jordan Derivations on Triangular Algebras

On a noncommutative ring with identity and characteristic not equal to 2, we consider the Jordan derivation of triangular algebra. Using module theory and direct sum decomposition, we obtain that the Jordan derivation is a mapping from triangular algebra to bimodule, so it is a derivation, and it is also the result of the addition of a bimodule derivation and an internal derivation.