Corollary

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

The integral closure of an integral domain A is an integrally closed domain.

Let K be the field of fractions of A and B the integral closure of A. Clearly

K is the field of fractions of B and it is sufficient to apply Proposition 7 to $R = K$ .

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

Cited by

Nothing.