Unformatted text preview: α be the real number such that α 4 = 5. (a) Show that Q ( iα 2 ) is normal over Q . (b) Show that Q ( α + iα ) is normal over Q ( iα 2 ). (c) Show that Q ( α + iα ) is not normal over Q . 3. Show that K is perfect if and only if every algebraic extension of K is seperable. 1...
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 Spring '09
 SusamaAgarwala
 Math, Algebra, Prime number, Foote, Seperable, Normal ﬁeld

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