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Jordan superderivations. II

In a recent paper we have extended the classical Herstein's theorem on Jordan derivations on prime rings to Jordan superderivations on prime associative superalgebras. In the present paper we extend this result to semiprime associative superalgebras.

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