Lemma 10.36.3 (00GK)—The Stacks project

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Part 1: Preliminaries
Chapter 10: Commutative Algebra
Section 10.36: Finite and integral ring extensions
Lemma 10.36.3 (cite)

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Lemma 10.36.3. A finite ring map is integral.

Proof. Let $R \to S$ be finite. Let $y \in S$. Apply Lemma 10.36.2 to $M = S$ to see that $y$ is integral over $R$. $\square$

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