关于环的正则性

On the Regularity of Rings

利用环的拟理想对环的正则性进行了刻画,主要得到了两个结果:①设R是左SPF-环.若R的每一个极大的左理想是拟理想,则R/J(R)是强正则环.②设环R的每一个极大的左理想是拟理想,则以下等价:R是强正则环;R是广义正则的SI环;每一个单左R-模是GP-内射的.

In this paper, two results on the regularity of rings characterized by their quasi-ideal are mainly obtained： ①If R is a left SPF-ring whose every maximal left ideal is a quasi-ideal,then R/J（R ）is a strongly R is a ring whose every maximal left ideal is a quasi-ideal, then the following regular ring.②If statements are equivalent：R is a strongly regular ring. R is a generalized regular SI ring. Every simple left R -module is GP-injective.