The purpose of this paper is to characterize strongly regular rings via MERT rings and weakly one-sided ideals. Many important equivalent conditions on strongly regular rings are shown.
In this paper, some new relations between GP-V'-rings and regular rings under certain special conditions have been found. It is proved that R is left self-injective regular with Soc(RR) ≠ 0 if and only if R is a ...In this paper, some new relations between GP-V'-rings and regular rings under certain special conditions have been found. It is proved that R is left self-injective regular with Soc(RR) ≠ 0 if and only if R is a left GP-V'-ring containing an injective maximal left ideal and Soc(RR)(?)Soc(RR). Moreover, for an MELT ring R, it is shown that R is regular if and only if R is a left GP-injective left GP-V'-ring.展开更多
In this paper,we introduce a non-trivial generalization of ZI-rings-quasi ZI-rings.A ring R is called a quasi ZI-ring,if for any non-zero elements a,b ∈ R,ab = 0 implies that there exists a positive integer n such th...In this paper,we introduce a non-trivial generalization of ZI-rings-quasi ZI-rings.A ring R is called a quasi ZI-ring,if for any non-zero elements a,b ∈ R,ab = 0 implies that there exists a positive integer n such that an = 0 and anRbn = 0.The non-singularity and regularity of quasi ZI,GP-Vˊ-rings are studied.Some new characterizations of strong regular rings are obtained.These effectively extend some known results.展开更多
基金This work was supported in part by the NNSF (10071035) of China
文摘The purpose of this paper is to characterize strongly regular rings via MERT rings and weakly one-sided ideals. Many important equivalent conditions on strongly regular rings are shown.
基金This work was partially support by the NNSF of China (No. 10171011) the NSF of JiangsuProvince in China (No. BK 2001001) the Younger Foundation (2003xqn04) of Anhui Normal University.
文摘In this paper, some new relations between GP-V'-rings and regular rings under certain special conditions have been found. It is proved that R is left self-injective regular with Soc(RR) ≠ 0 if and only if R is a left GP-V'-ring containing an injective maximal left ideal and Soc(RR)(?)Soc(RR). Moreover, for an MELT ring R, it is shown that R is regular if and only if R is a left GP-injective left GP-V'-ring.
基金Supported by the National Natural Science Foundation of China (Grant Nos.10871106 10901002+1 种基金 10971099)the Natural Science Foundation of Anhui Provincial Education Committee (Grant No.KJ2008A026)
文摘In this paper,we introduce a non-trivial generalization of ZI-rings-quasi ZI-rings.A ring R is called a quasi ZI-ring,if for any non-zero elements a,b ∈ R,ab = 0 implies that there exists a positive integer n such that an = 0 and anRbn = 0.The non-singularity and regularity of quasi ZI,GP-Vˊ-rings are studied.Some new characterizations of strong regular rings are obtained.These effectively extend some known results.
