Abstract
Let $F:R\rightarrow R$ be a generalized derivation of a 2-torsion free prime ring $R$ together with a derivation $d.$ In this paper, we show that a nonzero Jordan ideal $J$ of $R$ contains a nonzero ideal of $R$. Further, we use this result to prove that if $F([x, y])\in Z(R)$ for all $x, y\in J, $ then $R$ is commutative. Consequently, it extends a result of Oukhtite, Mamouni and Ashraf.
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