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Unformatted text preview: F 5 . (10 points) 7 8. Let E/K be a feld extension and let L be an intermediate feld. IF L is ( K, E )stable, prove that L 00 is ( K, E )stable, too. (15 points) 8 9. Find an algebraic feld extension that is not separable. (10 points) 9 10. Let ζ := e 2 πi 12 ∈ C and E := Q ( ζ ). Find all subgroups of G := Aut Q E , all intermediate ±elds of E/ Q , and a primitive element for each of the intermediate ±elds. Describe the Galois correspondence by Hasse diagrams of groups and intermediate ±elds. (20 points) 10 Bonus question. Tell about the contribution to algebra of one of the following mathematicians: Gauss, Cauchy, Abel, Liouville, Klein, Kronecker, Dedekind, Heinrich Weber, Artin. 11...
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 Spring '11
 ergenc
 Math, Galois theory, finite field

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