$E$ and $F$ have an arbitrary characteristic.
I'm stuck in this problem, i had some ideas, but they led me to nothing.
If anyone could give me some hint, some direction on how to do it, i would appreciate a lot.
The Definition of Separable extension is the Lang's definition:
- $E/F$ is separable if the number of possible extensions of an injective homomorphism $\sigma :F \rightarrow A$ (where's $A$ is an algebraically closed field) to an injective homomorphism of $E$ into $A$ is equal to $[E:F]$