Author/Authors :
Ashraf M. نويسنده Department of Mathematics,
Aligarh Muslim University,
Aligarh, 202002, India. , Parveen N. نويسنده Department of Mathematics,
Aligarh Muslim University,
Aligarh, 202002, India.
Abstract :
Let $R$ be a $*$-prime ring with center $Z(R)$, $d$ a non-zero $(sigma,tau)$-derivation of $R$ with associated automorphisms $sigma$ and $tau$ of $R$, such that $sigma$, $tau$ and $d$ commute with $ʹ*ʹ$. Suppose that $U$ is an ideal of $R$ such that $U^*=U$, and $C_{sigma,tau}={cin R~|~csigma(x)=tau(x)c~mbox{for~all}~xin R}.$ In the present paper, it is shown that if characteristic of $R$ is different from two and $[d(U),d(U)]_{sigma,tau}={0},$ then $R$ is commutative. Commutativity of $R$ has also been established in case if $[d(R),d(R)]_{sigma,tau}subseteq C_{sigma,tau}.$
