How can I prove the following statement?
If $R$ is a reduced Noetherian commutative ring, then every associated prime ideal of $R$ is a minimal prime ideal of $R$.
2026-03-25 22:04:46.1774476286
On associated prime ideals of reduced commutative rings $R$
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An associated prime consists entirely of zero divisors. You should be able to express the set of zero divisors of a reduced ring in terms of minimal prime ideals, and to say something about the number of minimal primes in a noetherian ring. At this point, hopefully the way is clear.