2018
Том 70
№ 4

# On generalized derivations satisfying certain identities

Albaş E.

Abstract

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: $$(i) \quad d[(x, y)] = [d(x), d(y)] \quad \text{for all} x, y \in R;$$ $$(ii) \quad d[(x, y)] = [d(y), d(x)] \quad \text{for all} x, y \in R;$$ $$(iii)\quad d([x, y]) = [d(x), d(y)] \text{either} d([x, y]) = [d(y), d(x)] \quad \text{for all} x, y \in R$$.

English version (Springer): Ukrainian Mathematical Journal 63 (2011), no. 5, pp 690-698.

Citation Example: Albaş E. On generalized derivations satisfying certain identities // Ukr. Mat. Zh. - 2011. - 63, № 5. - pp. 596-602.

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