A Note on the Generalized Jordan Triple Derivations on Lie Ideals in Semiprime Rings - Hongan, Motoshi; Rehman, Nadeem ur (Sarajevo Journal of Mathematics, 2024)
Let $R$ be an associative ring, and $F: R\longrightarrow R$ an additive mapping. The map $F$ is called a Jordan triple derivation if $F(xyx)=F(x)yx+xF(y)x+xyF(x)$ for all $ x,y \in R$ which is fulfilled \cite{3}, and $F$ is called a generalized Jordan triple derivation if $F(xyx)=F(x)yx+xf(y)x+xyf(x)$ with some Jordan triple derivation $f$ for all $ x, y \in R$ which is fulfilled \cite{JL}. In this note, we deal with generalized Jordan triple derivations of semiprime rings, and give an affirmative answer to our conjecture in \cite{HRA}. 2010 Mathematics Subject Classification. 16W25, 16N60, 16U80.