Corollary

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

Commutative Algebra, chapter VII, § 3. Factorial domains

If $A$ is a factorial domain, the domain $A[X_1, \ldots, X_n]$ is factorial.

Argue by induction on $n$ .

This corollary may be extended to the case of an infinite family of indeterminates (cf. Exercise 2).

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

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