# A note on generalized derivations on prime rings

Arabian Journal of Mathematics, Dec 2017

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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Maja Fošner, Nadeem ur Rehman, Tarannum Bano. A note on generalized derivations on prime rings, Arabian Journal of Mathematics, 2017, 1-5, DOI: 10.1007/s40065-017-0193-1