摘要
设R是半质环,C是R的中心。本文证明,当R满足下述条件之一时为交换环: 1.对任意x,y∈R,均有(xy)~2+x^2y^2∈C; 2.对任意x,y∈R,均有(xy)~2+y^2x^2∈C; 3.有整数n>1,m>1,使对任意x,y∈R,均有[X^n,y)-[x,y^n]∈C,且R为(M^n-m)-扭自由的。 我们定义环R的m-超中心为T_m={r∈R|对任意x∈R,均有rx^m=x^mr}。本文证明,若R为半质环,则T_m即为R的中心。
In this paper we proved: Let R be a semiprime ring and C be the centre of R, then R is commutative if R satisfies one of the following conditions:1. (xy)~2+x^2y^2∈C for every x, y∈R.2. (xy)~2+y^2x^2∈C for every x, y∈R.3. There exist integers n>1, m>1 such that [x^n, y]-[x, y^n]∈C for every x, y∈R and R is (m^n-m)-torsion free.We defined that the m-hypercentre of R is T_m={r∈R|rx^m=x^mr for every x∈R} and proved: If R is a semiprime ring, then T_m is just the centre of R.
出处
《吉林大学学报（理学版）》
CAS
1983年第2期19-25,共7页
Journal of Jilin University:Science Edition
