# Math Help - separable extension and separable polynomial

1. ## separable extension and separable polynomial

If $E$is a splitting field over $F$of a separable polynomial, why $E$is a separable extension of $F$ which means $\forall x\in E$, $x$is a root of a separable polynomial over $F$?

2. Originally Posted by ynj
If $E$is a splitting field over $F$of a separable polynomial, why $E$is a separable extension of $F$ which means $\forall x\in E$, $x$ is a root of a separable polynomial over $F$?
the proof of this theorem can be found in any textbook in field theory. the idea is to prove, by induction over $[E:F],$ that $|\text{Aut}_F(E)|=[E:F].$

3. Em..I am sorry that I do not fully understand whay my book is saying..but now I understand...