I was wondering for what kind of commutative rings we can always construct an infinite descending chain of distinct prime ideals?
When do infinite descending chains of prime ideals exist in commutative rings?
3
$\begingroup$
ring-theory
-
2One 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