Let $A$ be a Noetherian ring, and let $n$ be a fixed natural number. Show that there are only finitely many primes $P$ of $A$ such that the cardinality of $A/P \leq n$.
Prime ideals in noetherian rings have a property: if we have one prime ideal strictly in between two prime ideals, then we have infinitely many primes between them. Noetherian rings and prime ideals
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