The Stacks project

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. $\square$

Comments (1)

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.

Post a comment

Your email address will not be published. Required fields are marked.

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).

Unfortunately JavaScript is disabled in your browser, so the comment preview function will not work.

All contributions are licensed under the GNU Free Documentation License.




In order to prevent bots from posting comments, we would like you to prove that you are human. You can do this by filling in the name of the current tag in the following input field. As a reminder, this is tag 074W. Beware of the difference between the letter 'O' and the digit '0'.



View Lemma 11.7.4 as pdf