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I was wondering for what kind of commutative rings we can always construct an infinite descending chain of distinct prime ideals?

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    One example is $R[X_1,X_2,\ldots]$ for a domain $R$. There we have the infinite descending chain of prime ideals $I_1 \supsetneq I_2 \supsetneq \ldots $ with $I_k = (X_k, X_{k+1},\ldots)$.2012-03-14

2 Answers 2