Lemma 10.112.4 (00OK)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 10: Commutative Algebra
Section 10.112: Homomorphisms and dimension
Lemma 10.112.4 (cite)

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Lemma 10.112.4. Suppose $R \subset S$ and $S$ integral over $R$ . Then $\dim (R) = \dim (S)$ .

Proof. This is a combination of Lemmas 10.36.22, 10.36.17, 10.112.1, and 10.112.3. $\square$

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