关于周期环的若干结果

Some Results Concerning Periodic Rings

环Ｒ为周期环，如果对每一ｘ∈Ｒ有正整数ｍ（ｘ）≠ｎ（ｘ），使ｘｍ（ｘ）＝ｘｎ（ｘ）。本文给出周期环的若干结构定理，推广和改进了谢邦杰［１］，Ａｂｕ－ＫｈｕｚａｍａｎｄＹａｑｕｂ［２］和樊复生［３］的结果。

A ring R is called a periodic ring, if for every x∈R there is a pair m(x), n (x) of distinct positive integers such that xm(x)=xn(x).In this paper, some theorems concerning structure of periodic rings arc given.These results generalize and improve results obtained by Xie Bangjie[1] and Abu-Khzam and Yaqub[2] and Fan Fusheng [3].