ON WEAKLY REGULAR RINGS AND GENERALIZATIONS OF V-RINGS

Authors : Tikaram Subedi, A M Buhphang

Pages : 162-173

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Publication Date : 2011-12-01

Article Type : Research Paper

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