
theorem Th33:
  for F being Field holds F is Noetherian
proof
  let F be Field;
  let I be Ideal of F;
  per cases by IDEAL_1:22;
  suppose
A1: I = {0.F};
    reconsider s0F = {0.F} as finite non empty Subset of F;
    {0.F} = s0F-Ideal by IDEAL_1:47;
    hence thesis by A1;
  end;
  suppose
A2: I = the carrier of F;
    reconsider s1F = {1_F} as finite non empty Subset of F;
    the carrier of F = s1F-Ideal by IDEAL_1:51;
    hence thesis by A2;
  end;
end;
