Example 2

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

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

Let $R'$ be a sub-A-algebra of $R$ ; the elements of $R'$ which are integral over $A$ are just the elements of $R$ which are integral over $A$ and belong to $R'$ ; this often allows us not to specify the algebra to which an integral element over $A$ belongs, when no confusion can arise.

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

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