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This question already has an answer here:

Let K be a field with char(K)>0.

How do I prove that every algebraic extension of K is a separable extension if and only if $\phi:x \rightarrow x^p$ is surjective ?

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marked as duplicate by Alexander Gruber Jan 16 '15 at 18:06

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • $\begingroup$ Hello, this is only one direction and it seems for me that the assumptions are not the same in the other question. $\endgroup$ – Joundi Jan 16 '15 at 18:54