Lemma 9.15.3 (09HP)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 9: Fields
Section 9.15: Normal extensions
Lemma 9.15.3 (cite)

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Lemma 9.15.3. Let $F$ be a field. Let $M/F$ be an algebraic extension. Let $M/E_ i/F$ , $i \in I$ be subextensions with $E_ i/F$ normal. Then $\bigcap E_ i$ is normal over $F$ .

Proof. Direct from the definitions. $\square$

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