Math 514 homework #12 Due date: 19951009 D. J. Bernstein 19951001 Exercise 41. Let R be a Dedekind domain. Let I be a nonzero ideal of R. Prove that I = ∏ Q^{ord_{Q} I}, where Q ranges over the nonzero prime ideals of R. Exercise 42. Let R be a Dedekind domain, let F be the field of fractions of R, and let x be an element of F. Assume that v(x) ≥ 0 for every valuation v on F. Prove that x ∈ R.