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Graduate Algebra Study Notes II-(17)

Key Words: Fields, Galois Theory, Spitting Fields, Algebraic Closure, Normality

(18) Let F be normal over K and E an intermediate field. Then E is normal over K if and only if E is stable.
(22) If F is algebraic over K and every element of F belongs to an intermediate field that is normal over K, then F is normal over K.
(23) If [F:K]=2, then F is normal over K.
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