GWCN环的一些研究

On GWCN Rings

本文主要讨论了GWCN环的若干性质以及它与一些特殊环的关系,研究了GWCN环的强正则性,证明了:若R是有Abelian极大左理想的GWCN环,那么下列条件等价:(1)R是强正则环;(2)R为左GP-V’-环,且R的极大本质左理想均为广义弱理想;(3)R是左GP-V’-环,且R的极大本质右理想均为广义弱理想.

In this paper, we give some properties of GWCN rings and the relationships between GWCN rings and other special rings. The strong regularity of GWCN rings is studied. We mainly obtain that if R has an Abelian maximal left ideal and R is a GWCN ring, then R is strongly regular if and only if R is a left GP-V＇-ring whose maximal essential left ideals are GW-ideals if and only if R is a left GP-V＇-ring whose maximal essential right ideals are GW-ideals.