Jordan Derivations of Special Subrings of Matrix Rings

Abstract

Let $K$ be a 2-torsion free ring with identity and $R_n(K,J)$ be the ring of all $n\times n$ 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 $R_n(K,J).$

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