
theorem
for F being Field
for E being FieldExtension of F
holds E is F-algebraic iff
      for a being Element of E holds FAdj(F,{a}) is F-finite
proof
let F be Field, E be FieldExtension of F;
now assume A: for a being Element of E holds FAdj(F,{a}) is F-finite;
  now let a be Element of E;
    FAdj(F,{a}) is F-finite by A;
    hence a is F-algebraic by FIELD_6:68;
    end;
  hence E is F-algebraic;
  end;
hence thesis;
end;
