On generalized derivations satisfying certain identities

  • E. Albaş Ege Univ., Izmir, Turkey

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: $$(i) \quad d[(x, y)] = [d(x), d(y)] \quad \text{for all} x, y \in R;$$ $$(ii) \quad d[(x, y)] = [d(y), d(x)] \quad \text{for all} x, y \in R;$$ $$(iii)\quad d([x, y]) = [d(x), d(y)] \text{either} d([x, y]) = [d(y), d(x)] \quad \text{for all} x, y \in R$$.
Published
25.05.2011
How to Cite
Albaş, E. “On Generalized Derivations Satisfying Certain Identities”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, no. 5, May 2011, pp. 596-02, https://umj.imath.kiev.ua/index.php/umj/article/view/2745.
Section
Research articles