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I'm suppossed to use an example to show the following statement. If F over K is galois but not algebraic and L is an intermediate field between K and F, then F over L is not galois. Any help at all would be greatly appreciated.

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    The most common definition of "Galois extension" requires that the extension be algebraic. What definition are you using?2011-03-28
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    @ Brad I think that F must have char 02011-03-28
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    @user8771, a Galois extension may well be infinite but it still needs to be algebraic under the common definition. Also, if F is an extension of K and L is an intermediate field, then "K over L" doesn't make sense.2011-03-28
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    Thank you..I just edited it.2011-03-28
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    Ok, that still leaves the question of what "Galois but not algebraic" means. Whatever the definition, the question seems odd - F/L is not Galois for all L except L=K?2011-03-28
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    @All Hungerford's Algebra book defines a Galois extension as an extension $F/K$ such that the fixed field of $\text{Aut}_K F$ is $K$, without requiring it to be algebraic, although he explicitly notes that it is commonly required to be algebraic.2011-03-28

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