How's this inertia called?

Question

Let $E/F$ be an algebraic extension.

Let $L_1,L_2$ be algebraically closed fields and $\sigma_1:F\rightarrow L_1,\sigma_2:F\rightarrow L_2$ be field monomorphisms.

Define $A=\{\tau_1|\tau_1:E\rightarrow L_1 \text{ is a field monomorphism and an extension of } \sigma_1\}$

Define $B=\{\tau_2|\tau_2:E\rightarrow L_2 \text{ is a field monomorphism and an extension of } \sigma_2\}$.

Then, it can be shown that $|A|=|B|$.

Hence, it's possible to define this cardinality as ${E:F}$ when an algebraic extension $E/F$ is given.

What is the name of ${E:F}$? And how is it called? Is there an article about this number in wikipedia?

Answer 1

I believe the value you are asking about is the $\textbf{separable degree}$.

Read the comments and answers at this previous question for more information. This is a very important concept in field theory.