On the Krull dimension of rings of integer-valued rational functions
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910739212533760 |
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| author | Chems-Eddin, Mohamed Mahmoud Feryouch, Badr Mouanis, Hakima Tamoussit, Ali |
| author_facet | Chems-Eddin, Mohamed Mahmoud Feryouch, Badr Mouanis, Hakima Tamoussit, Ali |
| contents | Let $D$ be an integral domain with quotient field $K$ and $E$ a subset of $K$. The \textit{ring of integer-valued rational functions on} $E$ is defined as $$\mathrm{int}_R(E,D):=\lbrace φ\in K(X);\; φ(E)\subseteq D\rbrace.$$ The main goal of this paper is to investigate the Krull dimension of the ring $\mathrm{int}_R(E,D).$ Particularly, we are interested in domains that are either Jaffard or PVDs. Interesting results are established with some illustrating examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_07931 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Krull dimension of rings of integer-valued rational functions Chems-Eddin, Mohamed Mahmoud Feryouch, Badr Mouanis, Hakima Tamoussit, Ali Commutative Algebra Let $D$ be an integral domain with quotient field $K$ and $E$ a subset of $K$. The \textit{ring of integer-valued rational functions on} $E$ is defined as $$\mathrm{int}_R(E,D):=\lbrace φ\in K(X);\; φ(E)\subseteq D\rbrace.$$ The main goal of this paper is to investigate the Krull dimension of the ring $\mathrm{int}_R(E,D).$ Particularly, we are interested in domains that are either Jaffard or PVDs. Interesting results are established with some illustrating examples. |
| title | On the Krull dimension of rings of integer-valued rational functions |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2412.07931 |