Moment of inertia of ring about its diameter is I. Then, moment of inertia about an axis passing through centre perpendicular to its plane is:

moment of inertia about a diameter of a ring is   $I=\frac{M{r}^2}{2}$

Moment of inertia of a ring about an axis passing through its center and perpendicular to its plane is 

I'=Mr²=2I