Let be a ring having unit 1. Denote by the center of . Assume that the characteristic of is not 2 and there is an idempotent element such that . It is shown that, under some mild conditions, a map is a multiplicative Lie triple derivation if and only if for all , where is an additive derivation and is a map satisfying for all . As applications, all Lie (triple) derivations on prime rings and von Neumann algebras are characterized, which generalize some known results.
Xiaofei Qi. "Characterization of Multiplicative Lie Triple Derivations on Rings." Abstr. Appl. Anal. 2014 1 - 10, 2014. https://doi.org/10.1155/2014/739730