摘要
本文证明了如果R是一个s-单式环,且满足条件:1.?x,y∈R,存在不全为1有有界正整数k=k(x,y),s=s(x,y),t=t(x,y)使得(xy)~k=x^sy’,(xy)^(k+1)=x^(s+1)y^(t+1);2.R的所有幂零元素集合N是p-扭自由的,这里p是诸s和t的最小公倍数,则R是交换环。
In this paper, the following commutativity condition on rings is proved:Let R be a s-unital ring, if there exist bounded positive integers k=k(x, y), s=s(x,y),t=t(x,y) (at least one≠1) such that (xy)~k=x^sy^t,(xy)^(k+1)=x^(s+1)y^(t+1) forany x,y∈R, and the set of nilpotent elements in R be p-torbion free, here p bethe least common multiple of all k, s, t, then R is commutative.
出处
《湖南教育学院学报》
1994年第5期104-106,共3页
Journal of Hunan Educational Institute
关键词
交换性
结合环
S单式环
s-unital ring
p-torsion free
commutativity