Tri-additive maps and local generalized $(α,β)$-derivations

  • M. R. Jamal
  • M. R. Mozumder


Let $R$ be a prime ring with nontrivial idempotents. We characterize a tri-additive map $f : R^3 \rightarrow R$ 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, any local generalized $(\alpha , \beta)$-derivation (or a generalized Jordan triple $(\alpha , \beta)$-derivation) is a generalized $(\alpha , \beta)$-derivation.
How to Cite
Jamal, M. R., and M. R. Mozumder. “Tri-Additive Maps and Local Generalized $(α,β)$-Derivations”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 69, no. 6, June 2017, pp. 848-53,
Short communications