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Clarifying question about 1.(2) and 3.(3) on HW2.

Clarifying question about 1.(2) and 3.(3) on HW2.

av Benjamin Andersson -
Antal svar: 4

Hi, should one assume that sigma fixes F in 1.(2) and 3.(3), or just that sigma(F) = F, if that question makes sense. I have a proof in 3.(3) under the assumption that Aut(F(x)/F(x^p)) is meant, but naively I would interpret sigma:E ---> E that is an F-automorphism as F only needs to send F to F bijectively, not neccessarily be the identity on F.


That is, when you say that we have an automorphism E/F such that it is an F-automorphism, do you mean that it is the identity on F, or just takes F to F bijectively?

Best,

Ben

Som svar till Benjamin Andersson

Re: Clarifying question about 1.(2) and 3.(3) on HW2.

av Sofia Tirabassi -
Sorry, I relooked at the homework sigm(K)=K means just that sigma sends K in K, not that it us the identity on K.

On the other side, when I speak of F-automorphism or of an automorphism that fixes F, I mean an automorphism that is the identity on F