I'm trying to solve an exercise.
I should prove that if $R$ is a notherian ring and $\operatorname{Spec}(R)$ is discrete then $R$ is artinian.
I think it is enough to show that $\dim R=0$ since I can use that $R$ is artinian if and only if $R$ is noetherian and $\dim R=0$. Can you help me?
Thank you!