Document Type : Research Paper
Department of mathematics, Faculty of science & Arts-Rabigh, King Abdulaziz University, Jaddeh 21589, Saudi Arabia
Department of mathematics, Aligarh Muslim University, Aligarh-202002, Aligarh, India
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.