Generalized Jordan derivations on semiprime rings

Abstract

The purpose of this note is to prove the following. Suppose $\mathbb{R}$ is a semiprime unity ring having an idempotent element e $\left(e\ne 0,e\ne 1\right)$ which satisfies mild conditions. It is shown that every additive generalized Jordan derivation on $\mathbb{R}$ is a generalized derivation.

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