Lemma 9.9.2. The degree of the minimal polynomial is $[k(\alpha ) : k]$.
Proof. This is just a restatement of the argument in Lemma 9.6.8: the observation is that if $P$ is the minimal polynomial of $\alpha $, then the map
is an isomorphism as in the aforementioned proof, and we have counted the degree of such an extension (see Example 9.7.6). $\square$
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Your email address will not be published.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).
All contributions are licensed under the GNU Free Documentation License.