Von Neumann正则环的几点注记

本文利用理想化子的概念定义了duo环的一个推广,称为MD环,并且研究了MD环的一些性质.特别地.我们证明了:如果R是MD环,且每一个奇异单左R-模是p-内射的,那么R是指数有界的von Ncumann正则环,因此,R.Yue chi ming提出的如下公开问题得到了肯定的回答:GLD左Γ-环是否为Von ncumann正则的?

Some Remarks of Von. Neumann Regular Rings

In this paper, a generalization of duo rings, called MD rings, is introduced in terms of idealizers. Some properties of MD rings are considered. In particular, we proved that an MD ring whose simple singular left modules are p-injective is a Von Neumann regular ring of bounded index. Therefore, the following question raised by R. Yue Chi Ming is answered in the positive: Is R Von Neumann regular if R is a GLD left V-ring?