Corollary 1

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

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

With the hypotheses and notation of Proposition 21, if every homogeneous element of $S^{-1}\mathbf{A}$ which is integral over $\mathbf{A}$ belongs to $\mathbf{A}$ , then $\mathbf{A}$ is integrally closed.

Then $\mathbf{A}'_i \subset \mathbf{A}$ for all $i \in \mathbf{Z}$ and hence $\mathbf{A}' = \mathbf{A}$ .

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

Cited by

Corollary 3, § 1

Cites

Proposition 21