Radical factorization in higher dimension
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866914950046285824 |
|---|---|
| author | Spirito, Dario |
| author_facet | Spirito, Dario |
| contents | 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 $\mathcal{V}(I)\subseteq X$ 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 $\mathrm{Inv}(D)$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_10219 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Radical factorization in higher dimension Spirito, Dario Commutative Algebra 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 $\mathcal{V}(I)\subseteq X$ 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 $\mathrm{Inv}(D)$ 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. |
| title | Radical factorization in higher dimension |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2409.10219 |