On commutativity theorems for rings
نویسندگان
چکیده
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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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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Introduction. A celebrated theorem of N. Jacobson [7] asserts that if (1) x*(x) =x for every x in a ring R, where n(x) is an integer greater than one, then R is commutative. In a recent paper [2], I. N. Herstein has shown that it is enough to require that (1) holds for those x in R which are commutators: x= [y, z]=yz — zy of two elements of R. The purpose of this note is to show that if R has n...
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 1990
ISSN: 0161-1712,1687-0425
DOI: 10.1155/s0161171290000126