Proposition 3

Tag 051R, permanent. Cite it as [Bourbaki, Tag 051R].

Commutative Algebra, chapter VII, § 3. Factorial domains

Let A be a Krull domain and S a multiplicative subset of A not containing 0.

(i) If A is factorial, $S^{-1}A$ is factorial. (ii) If S is generated by a family of elements $p_i$ such that the principal ideals $Ap_i$ are prime and $S^{-1}A$ is factorial, then A is factorial.

This follows immediately from Definition 1 of no. 1 and § 1, no. 10, Proposition 17.

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

Cited by

Exercise 22, § 3
Exercise 25, § 3
Exercise 5, § 3
Exercise 7, § 3
Exercise 26, § 4

Cites

§ 1, no. 10, Proposition 17
Definition 1