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. $\square$

Comment #3030 by Brian Lawrence on

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

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