关于广义周期环的几个定理

摘要

A ring R is called a generalized periodic ring,if for every x∈R there exist a positive integer n=n(x)depending on x and a polynomial fx(t)∈Z[t]such that xn(x)=xn(x)+1fx(x).Generalized periodic tings with a unique nonzero idempotent element are characterized.%设R是结合环,如果对每个x ∈ R,有依赖于x的正整数n=n(x)及fx(t)∈Z[t]使得xn(x)=xn(x)+1fn(x),则称R为广义周期环.刻画了只有一个非零幂等元的广义周期环.