Tri-additive maps and local generalized (α,β)-derivations - Jamal, M. R.; Mozumder, M. R. (Ukrains’kyi Matematychnyi Zhurnal, 2017)
Let R be a prime ring with nontrivial idempotents. We characterize a tri-additive map f : R^3 → R such that f(x, y, z) = 0 for all x, y, z R with xy = yz = 0. As an application, we show that, in a prime ring with nontrivial idempotents, any local generalized (α , β)-derivation (or a generalized Jordan triple (α , β)-derivation) is a generalized (α , β)-derivation.