Original Article
Kyungpook Mathematical Journal 2005; 45(3): 357-362
Published online September 23, 2005
Copyright © Kyungpook Mathematical Journal.
Generalizations of V-rings
Xianmei Song1, Xiaobin Yin2
"1Department of Mathematics, Southeast University, Nanjing 210096, P. R. China 1Department of Mathematics, Anhui Normal University, Wuhu 241000, P. R. China
2Department of Mathematics, Anhui Normal University, Wuhu 241000, P. R. China
"
In this paper, we introduce a new notion which we call a generalized weakly ideal. We also investigate characterizations of strongly regular rings with the condition that every maximal left ideal is a generalized weakly ideal. It is proved that $R$ is a strongly regular ring if and only if $R$ is a left GP-V-ring whose every maximal left (right) ideal is a generalized weakly ideal. Furthermore, if $R$ is a left SGPF ring, and every maximal left (right) ideal is a generalized weakly ideal, it is shown that $R/J(R)$ is strongly regular. Several known results are improved and extended.
Keywords: GP-V-ring, GW-ideal, SGPF ring, strongly regular