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A note on generalized derivations on prime rings

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...

Approximate Cubic Lie Derivations

, Mariborska Cesta 7, 3000 Celje, Slovenia Received 11 April 2013; Accepted 27 June 2013 Academic Editor: Janusz Brzdek Copyright © 2013 Ajda Fošner and Maja Fošner. This is an open access article