类似于VNL环的环
SOME RINGS SIMILAR TO THE VNL RINGS

本文研究类似于VNL环的环的性质.称一个环R是几乎弱正则环（几乎π-正则环，几乎强π-正则环），如果对任意的a ∈ R，都有a或1-a是弱正则（π-正则，强π-正则）元.本文讨论这些新环的扩张，给出相关环之间的关系图，拓广了局部环和VNL环的研究.
In this paper, we investigate the properties of rings similar to the VNL rings. A ring R is said to be a almost weakly regular ring (almost π-regular ring, almost strongly π-regular ring), provided that for any a ∈ R, either a or 1-a is weakly regular (π-regular, strongly π-regular). We discuss extensions of these new rings and give the relationship between relevant rings, which extend the study of local rings and VNL rings