@article {
author = {Ashraf, M. and Parveen, N.},
title = {Some commutativity theorems for $*$-prime rings with $(\sigma,\tau)$-derivation},
journal = {Bulletin of the Iranian Mathematical Society},
volume = {42},
number = {5},
pages = {1197-1206},
year = {2016},
publisher = {Iranian Mathematical Society (IMS)},
issn = {1017-060X},
eissn = {1735-8515},
doi = {},
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 $'*'$. Suppose that $U$ is an ideal of $R$ such that $U^*=U$, and $C_{\sigma,\tau}=\{c\in R~|~c\sigma(x)=\tau(x)c~\mbox{for~all}~x\in R\}.$ 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 $[d(R),d(R)]_{\sigma,\tau}\subseteq C_{\sigma,\tau}.$},
keywords = {Prime-rings,derivations,ideal,involution map},
url = {http://bims.iranjournals.ir/article_874.html},
eprint = {http://bims.iranjournals.ir/article_874_0ec3eca69c4da52c1cf3357568f2b7fd.pdf}
}