2019
Том 71
№ 10

# Albaş E.

Articles: 1
Article (English)

### On generalized derivations satisfying certain identities

Ukr. Mat. Zh. - 2011. - 63, № 5. - pp. 596-602

Let $R$ be a prime ring with char $R \neq 2$ and $d$ be a generalized derivation on $R$. The goal of this study is to investigate the generalized derivation $d$ satisfying any one of the following identities: $$(i) \quad d[(x, y)] = [d(x), d(y)] \quad \text{for all} x, y \in R;$$ $$(ii) \quad d[(x, y)] = [d(y), d(x)] \quad \text{for all} x, y \in R;$$ $$(iii)\quad d([x, y]) = [d(x), d(y)] \text{either} d([x, y]) = [d(y), d(x)] \quad \text{for all} x, y \in R$$.