A result on generalized derivations on right ideals of prime rings

  • N. Argaç Ege Univ., Izmir, Turkey
  • Ç. Demir Ege Univ., Izmir, Turkey

Abstract

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 there exist $a, b \in U$ such that $G(x) = ax + xb$ for all $x \in R$ and one of the following assertions is true: $$(1)\quad (a - \lambda)I = (0) = (b + \lambda)I \;\;\text{for some}\; \lambda \in C,$$ $$(2)\quad (a - \lambda)I = (0) \;\;\text{for some}\; \lambda \in C \;\;\text{and}\; b \in C.$$
Published
25.02.2012
How to Cite
ArgaçN., and Demir Ç. “A Result on Generalized Derivations on Right Ideals of Prime Rings”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, no. 2, Feb. 2012, pp. 165-7, http://umj.imath.kiev.ua/index.php/umj/article/view/2563.
Section
Research articles