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
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.
