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Math Help - separable extension and separable polynomial

  1. #1
    ynj
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    separable extension and separable polynomial

    If Eis a splitting field over Fof a separable polynomial, why Eis a separable extension of F which means \forall x\in E, xis a root of a separable polynomial over F?
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    Quote Originally Posted by ynj View Post
    If Eis a splitting field over Fof a separable polynomial, why Eis 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].
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  3. #3
    ynj
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    Em..I am sorry that I do not fully understand whay my book is saying..but now I understand...
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