Math 514 homework #13 Due date: 19951011 D. J. Bernstein 19951001 Exercise 43. Let v be a valuation on some domain R. Prove that if v(x) < v(y) then v(x + y) = v(x). Exercise 44. Let v be a valuation on some domain R. Say f = gh for f, g, h ∈ R[x]. Write f = ∑ f_{i}x^{i}, g = ∑ g_{j}x^{j}, h = ∑ h_{k}x^{k}. Prove that min {v(f_{i})} = min {v(g_{j})} + min {v(h_{k})}.