## Taiwanese Journal of Mathematics

### DERIVATIONS AND CENTRALIZING MAPPINGS IN PRIME RINGS

Tsiu-Kwen Lee

#### Abstract

Let $R$ be a prime ring with extended centroid $C$ and $\rho$ a nonzero right ideal of $R$. In this paper we investigate the derivations $\delta$, $d$ on $R$ such that $[\delta (x), d(x)] \in C$ for all $x \in \rho$. As an application, we prove that any centralizing additive mapping $f$ on $\rho$ must be of the form $f(x)=\lambda x+\mu (x)$ for all $x\in\rho$, where $\lambda \in C$ and $\mu : \rho\to C$, except when $[\rho, \rho ]\rho =0$.

#### Article information

Source
Taiwanese J. Math., Volume 1, Number 3 (1997), 333-342.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500405693

Digital Object Identifier
doi:10.11650/twjm/1500405693

Mathematical Reviews number (MathSciNet)
MR1465935

Zentralblatt MATH identifier
0885.16021

#### Citation

Lee, Tsiu-Kwen. DERIVATIONS AND CENTRALIZING MAPPINGS IN PRIME RINGS. Taiwanese J. Math. 1 (1997), no. 3, 333--342. doi:10.11650/twjm/1500405693. https://projecteuclid.org/euclid.twjm/1500405693