Finally, it investigate QF-ring with right gpm-injective, and obtain the following theorem:Theorem The following statements are equivalent:(1) R is quasi-Frobeniusean ring:(2) R is right noetherian, left pm-injective ring, right pm-injective ring;(3) R is right noetherian, left pm-injective ring, right GP-injective ring;(4) R is right noetherian, left gpm-injective ring, right gpm-injective ring;(5) R is right noetherian, right gpm-injective ring and each right minimal ideal is right annihilator.

最后用右gpm-內射對QF環(huán)進行研究1024免费电影你懂的，得到了如下定理：定理下列條件等價：(1) R是quasi-Frobeniusean環(huán)欧美性爱生活；(2) R是右Noether，左pm-內射環(huán)影音先锋在线资源免费，右pm-內射環(huán)：(3) R是右Noether久久精品视频30，左pm-內射環(huán)，右GP-內射環(huán)禁止18随进入的网站；(4) R是右Noether国产孕妇一级A片免费观看，左gpm-內射環(huán)黄色av免费在线播放，右gpm-內射環(huán)亚洲精品自拍AV在线日韩；(5) R是右Noether，右gpm-內射環(huán)且每個極小右理想是右零化子影音先锋高清无码。

left annihilator：左零化子

left alternative ring 左交錯環(huán) | left annihilator 左零化子 | left artinian ring 左阿廷環(huán)