Commutativity results for rings
نویسندگان
چکیده
منابع مشابه
A COMMUTATIVITY CONDITION FOR RINGS
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.
متن کاملSome 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...
متن کاملa commutativity condition for rings
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.
متن کاملCommutativity for a Certain Class of Rings
We discuss the commutativity of certain rings with unity 1 and one-sided s-unital rings under each of the following conditions: xr[xs, y] = ±[x, yt]xn, xr[xs, y] = ±xn[x, yt], xr[xs, y] = ±[x, yt]ym, and xr[xs, y] = ±ym[x, yt], where r, n, and m are non-negative integers and t > 1, s are positive integers such that either s, t are relatively prime or s[x, y] = 0 implies [x, y] = 0. Further, we ...
متن کاملA Combinatorial Commutativity Property for Rings
Clearly, every commutative ring is a Qn-ring for arbitrary n; moreover, there exist badly noncommutative Qn-rings, since every ring with fewer than n elements is a Qnring. Our purpose is to identify conditions which force Qn-rings to be commutative or nearly commutative. It is obvious that every Qn-ring is a Pn-ring and every Pn-ring is a P∞-ring. We make no use of the results on Pn-rings in [1...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1988
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700027453