TY - JOUR AU - M. R. Jamal AU - M. R. Mozumder PY - 2017/06/25 Y2 - 2024/03/28 TI - Tri-additive maps and local generalized $(α,β)$-derivations JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 69 IS - 6 SE - Short communications DO - UR - https://umj.imath.kiev.ua/index.php/umj/article/view/1739 AB - 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, anylocal generalized $(\alpha , \beta)$-derivation (or a generalized Jordan triple $(\alpha , \beta)$-derivation) is a generalized $(\alpha , \beta)$-derivation. ER -