Similar to group graded rings and modules, partial semigroup graded rings and modules are defined.

The weakly graded periodic radical concept for general group graded rings is established, the fact that it is a graded special radical is proved and its graded module characterization is presented.

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.