Corollary 2

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

Commutative Algebra, chapter V, § 1. Notion of an integral element

Let $A$ be an integral domain. For the polynomial ring $A[X_1, \ldots, X_n]$ to be integrally closed, it is necessary and sufficient that $A$ be integrally closed.

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

Cited by

Proposition 19, § 1
Theorem 1 (Normalization Lemma), § 3

Cites

Nothing.