类似于VNL环的环  

SOME RINGS SIMILAR TO THE VNL RINGS

作　　者：王尧[1] 杨圳 任艳丽[2] WANG Yao;YANG Zhen;REN Yan-li(School of Mathematics and Statistics,Nanjing University of Information Science and Technology,Nanjing 210044,China;School of Information Engineering,Nanjing Xiaozhuang University,Nanjing 211171,China)

机构地区：[1]南京信息工程大学数学与统计学院,江苏南京210044 [2]南京晓庄学院信息工程学院,江苏南京211171

出　　处：《数学杂志》2018年第5期903-911,共9页Journal of Mathematics

基　　金：国家自然科学基金资助项目(11101217);江苏省自然科学基金资助项目(BK20141476)

摘　　要：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(almostπ-regular ring,almost stronglyπ-regular ring),provided that for any a∈R,either a or 1-a is weakly regular(π-regular,stronglyπ-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.

关 键 词：几乎弱正则环 几乎π-正则环 几乎强π-正则环 环扩张 

分 类 号：O153.3[理学—数学]