Corollary 1

Tag 04N1, permanent. Cite it as [Bourbaki, Tag 04N1].

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

Let $A$ be a ring, $B$ a (commutative) $A$ -algebra and $C$ a (not necessarily commutative) $B$ -algebra. Then every element $x \in C$ which is integral over $A$ is integral over $B$ .

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

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