A COMMUTATIVITY CONDITION FOR S-UNITAL RINGS

来源期刊：中南大学学报(英文版)1995年第2期

论文作者：Yin Zhiyun Huang Li

文章页码：81 - 83

Key words：s-unital rings; p-torsion free; commutativity

Abstract: Let R be an s-unital ring, and we prove a commutativity theorem of R satisfying the following conditions: (l ) For each x, y∈ R,there exist bounded positive integers k =k (x,y), s=s (x,y), t =t (x,y)(where, at least one of k, s, t is not equal to 1) such that (xy)^k=x^sy^t,(xy)^k+1 = x^s+1y^t+1 ;(2) N, the set of all nilpotent elements of R, is p-torsion free, where p is the L. C. M. (least common multiple) of all k, s, t.