Exercise 111.6.17. Show that if the ring $A$ is Noetherian then the topological space $\mathop{\mathrm{Spec}}(A)$ is Noetherian. Give an example to show that the converse is false. (The same for Artinian if you like.)
Exercise 111.6.17. Show that if the ring $A$ is Noetherian then the topological space $\mathop{\mathrm{Spec}}(A)$ is Noetherian. Give an example to show that the converse is false. (The same for Artinian if you like.)
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