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

中文翻译：

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半素环上的广义 JORDAN 推导

本笔记的目的是证明以下内容。认为$\mathfrak{R}$是具有幂等元素的半素单位环$e$($e\neq 0,~e\neq 1$) 满足温和条件。结果表明，每个加法广义 Jordan 推导$\mathfrak{R}$是广义推导。