Lemma 11.7.4 (074W)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 11: Brauer groups
Section 11.7: The centralizer theorem
Lemma 11.7.4 (cite)

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The dimension of a finite central skew field is the square of the dimension of any maximal subfield.

Lemma 11.7.4. Let $A$ be a finite central skew field over $k$ . Then every maximal subfield $K \subset A$ satisfies $[A : k] = [K : k]^2$ .

Proof. Special case of Lemma 11.7.3. $\square$

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Comment #3030 by Brian Lawrence on December 13, 2017 at 03:04

Suggested slogan: The dimension of a finite central skew field is the square of the dimension of any maximal subfield.

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