Jordan Derivations of Special Subrings of Matrix Rings

Let K be a 2-torsion free ring with identity and R-n (K, J) be the ring of all n x n matrices over K such that the entries on and above the main diagonal are elements of an ideal J of K. We describe all Jordan derivations of the matrix ring R-n (K, J) in this paper. The main result states that every Jordan derivation Delta of R-n (K, J) is of the form Delta = D + Omega, where D is a derivation of R-n (K, J) and Omega is an extremal Jordan derivation of R-n (K, J).