I have no work to show. This fact is presented in my book as an obvious corollary of the following theorem:
Theorem:
If I=$(p)$ is an non null ideal in A P.I.D, $I$ is prime iff it is maximal.
Thanks in advance, every help or hint is appreciated.
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Hint: what is the relationship between prime ideals, maximal ideals, fields, and integral domains? – Mark Saving Jan 13 '23 at 19:02
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@MarkSaving A/I is a field iff I is maximal in an integral domain, and so iff I is prime in a P.I.D – Luigi Jan 13 '23 at 19:04