Lemma 9.12.9. In Situation 9.12.7 we have $|\mathop{\mathrm{Mor}}\nolimits _ F(K, \overline{F})| = \prod _{i = 1}^ n \deg _ s(P_ i)$.

Proof. This follows immediately from Lemma 9.12.8. Observe that a key ingredient we are tacitly using here is the well-definedness of the separable degree of an irreducible polynomial which was observed just prior to Definition 9.12.6. $\square$

There are also:

• 2 comment(s) on Section 9.12: Separable extensions

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).