some commutativity theorems for $*$-prime rings with $(sigma,tau)$-derivation
نویسندگان
چکیده
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 $c_{sigma,tau}={cin r~|~csigma(x)=tau(x)c~mbox{for~all}~xin r}.$ 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 $[d(r),d(r)]_{sigma,tau}subseteq c_{sigma,tau}.$
منابع مشابه
Some commutativity theorems for $*$-prime rings with $(sigma,tau)$-derivation
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 $C_{sigma,tau}={cin R~|~csigma(x)=tau(x)c~mbox{for~all}~xin R}.$ In the present paper, it is shown that if charac...
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عنوان ژورنال:
bulletin of the iranian mathematical societyجلد ۴۲، شماره ۵، صفحات ۱۱۹۷-۱۲۰۶
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