Chapter 10 - Moments of Inertia - Section 10.8 - Mass Moment of Inertia - Problems - Page 571: 84

$I_z=R^2M$

We can find the moment of inertia of the ring about the z-axis as follows: $I_z=\int y^2 dm$ $\implies I_z=\int R^2 dm$ $\implies I_z=R^2\int dm$ As the total mass of the ring is M, therefore $M=\int dm$ $\implies I_z=R^2M$