Radical Factorization in Higher Dimension

We generalize the theory of radical factorization from almost Dedekind domain to strongly discrete Pr & uuml;fer domains; we show that, for a fixed subset X of maximal ideals, the finitely generated ideals with V(I) subset of 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 Pr & uuml;fer 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. (c) 2025 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http:// creativecommons.org/licenses/by-nc-nd/4.0/).