本文引入直投射覆盖的概念，证明了环R为左完全环当且仅当每一个左R-模（平坦左R-模）具有直投射覆盖；

This peper introduces the concept of direct-projective covers, and prove that a ring R is left perfect if and only if every left R-module(flat left R-module) has a direct-projective cover;

youdao

本文引入直投射覆盖的概念，证明了环R为左完全环当且仅当每一个左R-模（平坦左R-模）具有直投射覆盖；

This peper introduces the concept of direct-projective covers, and prove that a ring R is left perfect if and only if every left R-module(flat left R-module) has a direct-projective cover;

youdao