I claim that the Krull dimension of $Z[x]$ is $2$. I can produce a chain of length 2 as $(0)\subset (p)\subset (p,x)$ but how do I rigorously prove that there is no chain of length 3. Any help would be appreciated.
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5Perhaps you could try to find the maximal ideals of $\Bbb{Z}[x]$. – sharding4 Apr 15 '18 at 16:05
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Closing as an abstract duplicate as per the above suggestion. – KReiser Aug 16 '23 at 19:24