ON WEAKLY REGULAR RINGS AND GENERALIZATIONS OF V-RINGS

Abstract

In this paper, we have studied weakly regular rings and some generalizations of V-rings via GW-ideals. We have shown that: (1) If R is a left weakly regular ring whose maximal left (right) ideals are GW-ideals, then R is strongly regular; (2) If R is a right weakly regular ring whose maximal essential left ideals are GW-ideals, then R is ELT regular; (3) If R is a ring in which l(a) is a GW-ideal for all a ∈ R, then R is left weakly regular if and only if R is right weakly regular; (4) A ring R is strongly regular if and only if R is a ZI left GP-V′-ring whose maximal essential left (right) ideals are GW-ideals; (5) If R is a left (right) GP-V-ring such that l(a) is a GW-ideal for all a ∈ R, then R is weakly regular.