A result on generalized derivations on right ideals of prime rings

• Date: 2012
• Main Authors: Argaç, N., Demir, Ç., Аргац, Н., Демір, Ц.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2012
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2563
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

Let $R$ be a prime ring of characteristic not 2 and let $I$ be a nonzero right ideal of $R$. Let $U$ be the right Utumi quotient ring of $R$ and let $C$ be the center of $U$. If $G$ is a generalized derivation of $R$ such that $[[G(x), x], G(x)] = 0$ for all $x \in I$, then $R$ is commutative or t...