A classification of Prufer domains of integer-valued polynomials on algebras
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908871118815232 |
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| author | Peruginelli, Giulio Werner, Nicholas J. |
| author_facet | Peruginelli, Giulio Werner, Nicholas J. |
| contents | Let $D$ be an integrally closed domain with quotient field $K$ and $A$ a torsion-free $D$-algebra that is finitely generated as a $D$-module and such that $A\cap K=D$. We give a complete classification of those $D$ and $A$ for which the ring $\text{Int}_K(A)=\{f\in K[X] \mid f(A)\subseteq A\}$ is a Prüfer domain. If $D$ is a semiprimitive domain, then we prove that $\text{Int}_K(A)$ is Prüfer if and only if $A$ is commutative and isomorphic to a finite direct product of almost Dedekind domains with finite residue fields, each of them satisfying a double-boundedness condition on its ramification indices and residue field degrees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_09243 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A classification of Prufer domains of integer-valued polynomials on algebras Peruginelli, Giulio Werner, Nicholas J. Rings and Algebras Commutative Algebra 13F20, 13F05, 12J20, 13A18 Let $D$ be an integrally closed domain with quotient field $K$ and $A$ a torsion-free $D$-algebra that is finitely generated as a $D$-module and such that $A\cap K=D$. We give a complete classification of those $D$ and $A$ for which the ring $\text{Int}_K(A)=\{f\in K[X] \mid f(A)\subseteq A\}$ is a Prüfer domain. If $D$ is a semiprimitive domain, then we prove that $\text{Int}_K(A)$ is Prüfer if and only if $A$ is commutative and isomorphic to a finite direct product of almost Dedekind domains with finite residue fields, each of them satisfying a double-boundedness condition on its ramification indices and residue field degrees. |
| title | A classification of Prufer domains of integer-valued polynomials on algebras |
| topic | Rings and Algebras Commutative Algebra 13F20, 13F05, 12J20, 13A18 |
| url | https://arxiv.org/abs/2509.09243 |