2019
Том 71
№ 11

# Mozumder M. R.

Articles: 1
Brief Communications (English)

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

Ukr. Mat. Zh. - 2017. - 69, № 6. - pp. 848-853

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.