Proposition 13

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

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

Let $A$ be a ring, $\mathbf{R}$ an $A$ -algebra and $A'$ the integral closure of $A$ in $\mathbf{R}$ . Then the integral closure of $A[X_1, \ldots, X_n]$ in $\mathbf{R}[X_1, \ldots, X_n]$ is equal to $A'[X_1, \ldots, X_n]$ .

This follows from Proposition 12 and Definition 3 of no. 2.

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

Cited by

Corollary 1, § 1
Proposition 19, § 1

Cites

Definition 3
Proposition 12