The Strong Regularity Of J-rings And CN-rings

In this paper, the strong regularity of J-rings and CN-rings arestudied.This paper is composed of two chapters.The first chapter presents two examples that illustrate the rela-tionship between J-rings with reduced rings, ZI-rings and quasi ZI-rings.We mainly studied the the strong regularity of J-rings,we provedthat if R is a J-ring,then the following statements are equivalent:(1) R is a strongly regular ring;(2) R is a left(right) SF-rings;(3) R is a left GP-V-ring,and every maximal essential left(right)ideal of R is GW-ideal;(4) R is a left weakly regular ring,and every maximal essentialleft(right) ideal of R is GW-ideal.In the second chapter,we mainly studied the strong regularity ofCN-rings.Let R is a CN-ring,then the following statements are equiv-alent:(1) R is a strongly regular ring;(2) R is a left weakly regular ring,and every maximal essentialleft(right) ideal of R is GW-ideal.