2024/09/16 by Dario Spirito, Spirito, Dario · 1 citation
Mathematics · #Advanced Topics in Algebra #Rings, Modules, and Algebras #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.2409.10219
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 in the group Inv(D) of the invertible ideals of a strongly discrete Prüfer domains is often free: in particular, we show it when the spectrum of D is Noetherian or when D is a ring of integer-valued polynomials on a subset over a Dedekind domain.