reserve i,j for Nat;
reserve A,B for Ring;
reserve K, L for Field;

theorem Th34:
  for K,L be Field, w be Element of L st K is Subring of L holds
  ex g be Element of Polynom-Ring K st {g}-Ideal = Ann_Poly(w,K)
proof
  let K,L;
  let w be Element of L;
  assume
A0: K is Subring of L;
A1: Polynom-Ring K is PID;
  Ann_Poly(w,K) is Ideal of Polynom-Ring K by A0,Th33;
  hence thesis by A1,IDEAL_1:def 27;
end;
