Lemma 29.44.12 (035C)—The Stacks project

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Table of contents
Part 2: Schemes
Chapter 29: Morphisms of Schemes
Section 29.44: Integral and finite morphisms
Lemma 29.44.12 (cite)

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Lemma 29.44.12. A closed immersion is finite (and a fortiori integral).

Proof. True because a closed immersion is affine (Lemma 29.11.9) and a surjective ring map is finite and integral. $\square$

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