# On centralizers of prime rings with involution

Document Type : Research Paper

Authors

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

Main Subjects

### History

• Receive Date: 13 October 2012
• Revise Date: 12 September 2014
• Accept Date: 12 September 2014
• First Publish Date: 01 December 2015