相对投射复盖

RALATIVE PROJECTIVE COVER

推广了投射复盖的概念，定义了相对投射复盖，讨论了它存在的条件，得出了模Ａ有Ｍ—投射复盖当且仅当存在Ｍ—投射模Ｐ及满同态ｆ：Ｐ→Ａ，使得Ｋｅｒｆ≤ｏＰ。并利用它刻划了完全环，得出了环Ｒ为完全环当且仅当任意半单模Ａ有Ｒ（Ａ）—投射复盖。

The definition of projective cover is generalizated and the condition for the existence of M projective cover for every module A is given. The conclusion that the module A has M projective cover iff there is a M projective module p and an epimorphism f:P→A such that Ker f≤。P is obtained. Hence, we inscribe the perfect ring and obtain that the ring R is perfect iff every semisimple module A is R (A) projective cover.