Corollary 2

Tag 04Z7, permanent. Cite it as [Bourbaki, Tag 04Z7].

Commutative Algebra, chapter VII, § 1. Krull domains

Let $\mathbf{A}$ be a Krull domain. For a fractional ideal $\mathbf{a}$ of $\mathbf{A}$ to be divisorial, it is necessary and sufficient that it be the intersection of two fractional principal ideals.

The sufficiency is obvious (no. 1, Definition 2). The necessity follows from Corollary 1: take $b$ and $c$ to be principal and such that $b \supseteq a$ .

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

Cited by

Exercise 11, § 1
Proposition 15, § 1

Cites

no. 1, Definition 2
Corollary 1