Definition 6

Tag 0CK7, permanent. Cite it as [Bourbaki, Tag 0CK7].

Commutative Algebra, chapter VIII, § 1. Dimension de Krull d’un anneau

Let a be an ideal of a ring A. The codimension of V(a) in Spec(A) is called the height of the ideal a and is denoted by ht(a).

Assume that A is an integral domain. Then the prime ideals of height 1 of A in the sense of Definition 4 of VII, § 1, No. 6, are the prime ideals of height 1 in the sense of the above definition.

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

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