Radical factorization in higher dimension

We generalize the theory of radical factorization from almost Dedekind domain to strongly discrete Prüfer domains; we show that, for a fixed subset X of maximal ideals, the finitely generated ideals with V (I) ⊆ X have radical factorization if and only if X contains no critical maximal ideals with respect to X . We use these notions to prove that the group Inv (D) of the invertible ideals of a strongly discrete Prüfer domain is often free: in particular, we show it is free when the spectrum of D is Noetherian or when D is a ring of integer-valued polynomials on a subset over a Dedekind domain.