ON WEAKLY REGULAR RINGS AND GENERALIZATIONS OF V-RINGS
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: tsubedi2010@gmail.com (Tikaram Subedi) ardeline17@gmail.com (A. M. Buhphang)
- ISSN: 1306-6048
- Yayın Aralığı: Yılda 2 Sayı
- Başlangıç: 2007
- Yayıncı: Abdullah HARMANCI