Jordan Derivations of Special Subrings of Matrix Rings

Abstract

Let K be a 2-torsion free ring with identity and Rn(K, J) be the ring of all n × 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 Rn(K, J) in this paper. The main result states that every Jordan derivation Δ of Rn(K, J) is of the form Δ = D + Ω, where D is a derivation of Rn(K, J) and Ω is an extremal Jordan derivation of Rn(K, J).