Corollary

Tag 0CK9, permanent. Cite it as [Bourbaki, Tag 0CK9].

Let p be a prime ideal of A and S a multiplicative subset of A not meeting p. Then $\operatorname{ht}(p) = \operatorname{ht}(S^{-1}p)$ .

This follows from Proposition 7, a), and from II, § 2, No. 5, Proposition 11.

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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