On centralizers of prime rings with involution

Ali, S.; Dar, N. A.

On centralizers of prime rings with involution

Document Type : Research Paper

Authors

S. Ali ¹
N. A. Dar ²

¹ Department of mathematics‎, ‎Faculty of science & Arts-Rabigh‎, ‎King Abdulaziz University‎, ‎Jaddeh 21589‎, ‎Saudi Arabia‎

² Department of mathematics‎, ‎Aligarh Muslim University‎, ‎Aligarh-202002‎, ‎Aligarh‎, ‎India

Abstract

‎Let $R$ be a ring with involution $*$‎. ‎An additive mapping $T:R\to R$ is called a left(respectively right) centralizer if $T(xy)=T(x)y$ (respectively $T(xy)=xT(y)$) for all $x,y\in R$‎. ‎The purpose of this paper is to examine the commutativity of prime rings with involution satisfying certain identities involving left centralizers.

Keywords