Lemma 10.35.7. Let $R \to S$ be a ring homomorphism. The set

\[ S' = \{ s \in S \mid s\text{ is integral over }R\} \]

is an $R$-subalgebra of $S$.

Lemma 10.35.7. Let $R \to S$ be a ring homomorphism. The set

\[ S' = \{ s \in S \mid s\text{ is integral over }R\} \]

is an $R$-subalgebra of $S$.

**Proof.**
This is clear from Lemmas 10.35.4 and 10.35.3.
$\square$

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