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Let $A\rightarrow B$ be a ring homomorphism such that $B$ is a finitely generated $A$-module. How one shows that the (set-theoretic) fibers of the map $\operatorname{Spec}B\rightarrow\operatorname{Spec}A$, where the spectra are considered as topological spaces, are always finite?


marked as duplicate by user26857 abstract-algebra Dec 12 '16 at 20:20

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    $\begingroup$ This is related to the topic of integral extensions of rings, just in a different language. IIRC, just rephrase the problem in terms of prime ideals of $B$ lying over prime ideals of $A$. $\endgroup$ – user14972 Dec 12 '16 at 20:16