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 $x, y, z \in R$ with $xy = yz = 0$. As an application, we show that, in a prime ring with nontrivial idempotents, anylocal generalized $(α , β)$-derivation (or a generalized Jordan triple $(α , β)$-derivation) is a generalized $(α , β)$-derivation.