Question: Show that for F E F, E is a splitting field over F if and only if E contains all conjugates over F

Show that for F ≤ E ≤ F, E is a splitting field over F̅  if and only if E contains all conjugates over F in F̅  for each of its elements.

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Let E be a splitting field over F Let be in E but not in F By Corollary 506 the polynomial irr F spl... View full answer

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