关于π-正则环

研究π -正则环的性质 ,主要结果是 :(1)本原因式Artin的exchange环 ,如果同态半本原则必为幺正则环 .(2 )如果R是稳定度 1的π -正则环 ,则对任意的a∈R ,存在正整数n使an =e+u ,其中e2 =e ,u是R的可逆元 .特别 ,如果R是幺正则环 ,则Mn(R)是clean环 .

On Primitive Idempotents of the Strong Endomorphism Monoid of a Graph

In this paper, we describe the canonical partial order on the idempotent set of the strong endomorphism monoid of a graph, and using this we further characterize primitive idem potenes from the viewpoint of combinatorics. The number of them is also given.