Remark (1)

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

Commutative Algebra, chapter V, § 2. The lift of prime ideals

It follows from § 1, no. 3, Corollary to Proposition 11 that the integral closure of $A$ in $K'$ is the set of $x \in K'$ such that there exists $m \geq 0$ for which $x^{p^m} \in A$ (Algebra, Chapter V, § 8, no. 1, Proposition 1).

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

Cited by

Nothing.

Cites

§ 1, no. 3, Corollary to Proposition 11
Algebra, Chapter V, § 8, no. 1, Proposition 1