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: RR 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 R which is fulfilled 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 R which is fulfilled JL. In this note, we deal with generalized Jordan triple derivations of semiprime rings, and give an affirmative answer to our conjecture in HRA. 2010 Mathematics Subject Classification. 16W25, 16N60, 16U80.