Corollary 1

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

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

Let $A$ be an integral domain, $A'$ its integral closure and $S$ a multiplicative subset of $A$ such that $0 \notin S$ . Then the integral closure of $S^{-1}A$ is $S^{-1}A'$ .

The field of fractions $R$ of $A$ is also the field of fractions of $S^{-1}A$ since $0 \notin S$ (Chapter II, § 1, no. 1, Remark 7); Proposition 16 is then applied to $R$ .

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

Cited by

Lemma 4, § 1
Corollary 3, § 1
Corollary 4, § 1
Proposition 19, § 1

Cites

Proposition 16