Some commutativity theorems for $*$-prime rings with $(sigma,tau)$-derivation
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چکیده مقاله:
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...
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عنوان ژورنال
دوره 42 شماره 5
صفحات 1197- 1206
تاریخ انتشار 2016-11-01
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