Characterization of Multiplicative Lie Triple Derivations on Rings

Let R be a ring having unit 1. Denote by ZR the center of R. Assume that the characteristic of R is not 2 and there is an idempotent element e∈R such that aRe=0⇒a=00 and aR1-e=0⇒a=. It is shown that, under some mild conditions, a map L:R→R is a multiplicative Lie triple derivation if and only if L(x) = δ(x) + h(x) for all x∈R, where δ:R→R is an additive derivation and h:R→ZR is a map satisfying h([[a, b], c]) = 0 for all a,b,c∈R. As applications, all Lie (triple) derivations on prime rings and von Neumann algebras are characterized, which generalize some known results.