
theorem main1:
for F being Field,
    E being F-finite FieldExtension of F
holds E is F-normal iff
      ex p being non constant Element of the carrier of Polynom-Ring F
      st E is SplittingField of p
proof
let F be Field, E be F-finite FieldExtension of F;
now assume ex p being non constant Element of the carrier of Polynom-Ring F
      st E is SplittingField of p; then
  for K being FieldExtension of E
  for h being F-fixing Monomorphism of E,K holds h is Automorphism of E
    by lemNor2;
  hence E is F-normal by lemNor3;
  end;
hence thesis by lemNor1;
end;
