Abstract
Let R be a prime ring with the extended centroid C and symmetric Martindale quotient ring \(Q_s(R)\). In this paper we prove the following result. Let \(F: R \rightarrow R\) be a generalized derivation associated with a non-zero derivation d on R and let h be an additive map of R such that \(F(x)x=xh(x)\) for all \(x\in R\). Then either R is commutative or \(F(x)=xp\) and \(h(x)=px\) where \(p\in Q_{s}(R)\).
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Fošner, M., ur Rehman, N. & Bano, T. A note on generalized derivations on prime rings. Arab. J. Math. 7, 189–193 (2018). https://doi.org/10.1007/s40065-017-0193-1
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DOI: https://doi.org/10.1007/s40065-017-0193-1