Let $E/F$ be a finite extension and $F$ be a perfect field.

Here, perfect field means $char(F)=0$ or $char(F)=p$ and $F^p=F$.

How to prove $E$ is also perfect field?

For $char(F)=0$ case, it's trivial, but for $char(F)=p$, no improvement at all...

Give me some hints


Hint: Recall that a field is perfect if and only if every finite extension is separable. Now, if $L/E$ finite weren't separable, then clearly $L/F$ is finite and isn't separable.

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