关于周期环的几个定理

Several theorem concerning periodic rings

设R是结合环,如果对每一x∈R,有依赖于x的不同的正整数m=m(x),n=n(x),使得x^m=x^n,则称R为周期环。对只有一个非零幂等元的周期环进行刻画,给出只有一个非零幂等元的周期环的结构定理,推广文献[1]中的结果。

Let R be an associative ring. If for every x∈R there are distinct positive integers m=m(x) and n=n(x) such that x^m=x^n, then R is called a periodic ring. Periodic rings with unique non-zero idempotent element are characterized. The structure theorems for periodic rings with unique non-zero idempotent element are given The obtained results generalized those in [1].