Characterization of Multiplicative Lie Triple Derivations on Rings

Abstract EN

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=0 and aR1-e=0⇒a=0.

It is shown that, under some mild conditions, a map L:R→R is a multiplicative Lie triple derivation if and only if Lx=δx+hx for all x∈R, where δ:R→R is an additive derivation and h:R→ZR is a map satisfying ha,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.