共查询到16条相似文献,搜索用时 31 毫秒
1.
2.
3.
4.
5.
定理1 设R是半质环,m,n是固定正整数,且n>1.如果R满足条件(xmy)n-xmy∈Z(R),?x,y∈R,则R是交换环.定理2 设R是半质环,m,n,s,t是固定正整数,且(m+n)t=s+1,mt>1.如果R满足条件[xm,yn]t-[x,ys]∈Z(R),?x,y∈R,则R是交换环. 相似文献
6.
7.
设R表示结合环(可以没有单位元),Z(R)为环R的中心,对任意x·y∈R,[x,y]=xy-yx,郭元春证明了满足(xy)^2-xy^2x∈Z(R)的半质环是交换环,魏宗宣用类似的方法证明了满足(xy)^2-yx^2y∈Z(R)的半质环是交换环,我们推广上述结果,证明了下面的定理。 相似文献
8.
9.
10.
11.
定理1设R是半值环,n为固定的正整数,如果R满足条件:存在依赖于(?)x,y的两个字k(X,Y),t(X,Y),其中|k|X>1,|t|X=1,|k|Y≥|t|Y,|t|Y≤n,使k(x,y)-t(x,y)∈I(R),则R是交换环。定理2设R是半值环,如果R满足条件:存在正整数m=m(x,y)>1,n=n(y),使得(xny)m-x 相似文献
12.
Commutativity of Rings with Constraints Involving a Subset 总被引:1,自引:0,他引:1
Moharram A. Khan 《Czechoslovak Mathematical Journal》2003,53(3):545-559
Suppose that R is an associative ring with identity 1, J(R) the Jacobson radical of R, and N(R) the set of nilpotent elements of R. Let m 1 be a fixed positive integer and R an m-torsion-free ring with identity 1. The main result of the present paper asserts that R is commutative if R satisfies both the conditions(i) [x
m, y
m] = 0 for all
and(ii) [(xy)
m
+ y
m
x
m, x] = 0 = [(yx)
m
+ x
m
y
m, x], for all
This result is also valid if (i) and (ii) are replaced by (i) [x
m, y
m] = 0 for all
and (ii) [(xy)
m
+ y
m
x
m, x] = 0 = [(yx)
m
+ x
m
y
m, x] for all
Other similar commutativity theorems are also discussed. 相似文献
13.
14.
15.
本证明了以下定理:一个半素环是交换的当且仅当以下条件之一成立:(1)[x^my^n xy^nx,x]=0,(2)[x^sy^t yx^s,x]=0.其中x,y为R的任意元,m,n,s,t为正整数。 相似文献