Corollary
Tag 04NB, permanent. Cite it as [Bourbaki, Tag 04NB].
Commutative Algebra, chapter V, § 1. Notion of an integral element
Let A be a ring and R, R' two (commutative)A-algebras integral over A. Then R R' is integral over A.
is integral over R (Proposition 5) and hence the conclusion follows from Proposition 6.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
Cited by
Nothing.