• Kyungpook Mathematical Journal
• /
• v.45 no.3
• /
• pp.357-362
• /
• 2005

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.