Next, the concept of graded semiflat module is introduced and proved that K is a group-graded weakly regular ring if and only if all right K-module is graded semiflat module.

The main problems solved are that the flat decompositions are generalized to FP-flat decompositions, and some important properties of FP-flat modulus are described through dimensions in another way.

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;