Graded Injective Domains
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918030733213696 |
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| author | Hensler, Mike Klawa, Hannah |
| author_facet | Hensler, Mike Klawa, Hannah |
| contents | An integral domain $R$ is an $i$-domain if for every overring $S$ of $R$, $\text{Spec}(S) \rightarrow \text{Spec}(R)$ is injective and is a mated integral if for every overring $S$ of $R$ and prime ideal $P$ of $R$ such that $PS \neq S$, there exists exactly one prime ideal $Q$ of $S$ such that $Q \cap R = P$. In this paper, we explore graded notions of $i$-domains and mated domains and their connection with gr-Prüfer domains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_16143 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Graded Injective Domains Hensler, Mike Klawa, Hannah Commutative Algebra 13G05 (Primary) 13A02, 13A15, 13B30, 13F05 (Secondary) An integral domain $R$ is an $i$-domain if for every overring $S$ of $R$, $\text{Spec}(S) \rightarrow \text{Spec}(R)$ is injective and is a mated integral if for every overring $S$ of $R$ and prime ideal $P$ of $R$ such that $PS \neq S$, there exists exactly one prime ideal $Q$ of $S$ such that $Q \cap R = P$. In this paper, we explore graded notions of $i$-domains and mated domains and their connection with gr-Prüfer domains. |
| title | Graded Injective Domains |
| topic | Commutative Algebra 13G05 (Primary) 13A02, 13A15, 13B30, 13F05 (Secondary) |
| url | https://arxiv.org/abs/2505.16143 |