Some commutativity results for rings with two-variable constraints
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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In this paper, we use the structure theory to prove an analog to a well-known theorem of Herstein as follows: Let R be a ring with center C such that for all x,y ? R either [x,y]= 0 or x-x [x,y]? C for some non negative integer n= n(x,y) dependingon x and y. Then R is commutative.
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In this paper, we establish some commutativity theorems for certain rings with polynomial constraints as follows: Let R be an associative ring, and for all x, y ∈ R, and fixed non-negative integers m > 1, n ≥ 0, r > 0, s ≥ 0, t ≥ 0, p ≥ 0, q ≥ 0 such that P (x, y) = ±Q(x, y), where P (x, y) = ys[x, y]yt and Q(x, y) = xp[xm, yn]ryq. First,it is shown that a semiprime ring R is commutative if and...
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in this paper, we use the structure theory to prove an analog to a well-known theorem of herstein as follows: let r be a ring with center c such that for all x,y ? r either [x,y]= 0 or x-x [x,y]? c for some non negative integer n= n(x,y) dependingon x and y. then r is commutative.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1975
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1975-0382357-9