On Weakly Regular Rings and Generalizations of V-rings

  • Tikaram Subedi, A. M. Buhphang
  • Published 2011

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. Mathematics Subject Classification (2010): 16E50, 16D25, 16D40,16D50

Cite this paper

@inproceedings{Subedi2011OnWR, title={On Weakly Regular Rings and Generalizations of V-rings}, author={Tikaram Subedi and A. M. Buhphang}, year={2011} }