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

theorem Th39:
  for K,L be Field, w be Element of L st K is Subring of L &
  w is_integral_over K holds Ann_Poly(w,K) is prime
  proof
    let K,L;
    let w be Element of L;
    assume K is Subring of L & w is_integral_over K;
    then Ann_Poly(w,K) is proper quasi-prime by Th38,Th33;
    hence thesis;
  end;
