ON WEAKLY REGULAR RINGS AND GENERALIZATIONS OF V-RINGS

Year 2011, Volume: 10 Issue: 10, 162 - 173, 01.12.2011

Tikaram Subedi A. M. Buhphang

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.

Keywords

Von Neumann regular rings, strongly regular rings, weakly regular rings, GP-V-ring, GP-V′ -ring, GW-ideals

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• Tikaram Subedi and A. M. Buhphang Department of Mathematics North Eastern Hill University Permanent Campus Shillong-793022, Meghalaya, India. e-mails: [e-mail] (Tikaram Subedi) [e-mail] (A. M. Buhphang)