Lemma 10.60.4. The Krull dimension of R is the supremum of the heights of its (maximal) primes.
Proof. This is so because we can always add a maximal ideal at the end of a chain of prime ideals. \square
Lemma 10.60.4. The Krull dimension of R is the supremum of the heights of its (maximal) primes.
Proof. This is so because we can always add a maximal ideal at the end of a chain of prime ideals. \square
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