Corollary 2
Tag 04NK, permanent. Cite it as [Bourbaki, Tag 04NK].
Commutative Algebra, chapter V, § 1. Notion of an integral element
For a reduced Noetherian ring to be integrally closed in its ring of fractions it is necessary and sufficient that it be a direct composition of integrally closed (Noetherian) domains.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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