Local properties of integral domains under extensions and pullback constructions
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911376241328128 |
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| author | Baek, Hyungtae Lim, Jung Wook Ouzzaouit., Omar Tamoussit, Ali |
| author_facet | Baek, Hyungtae Lim, Jung Wook Ouzzaouit., Omar Tamoussit, Ali |
| contents | For a property $\mathcal{X}$ of integral domains, an integral domain $D$ is said to be a {\it locally $\mathcal{X}$-domain} if $D_P$ has the property $\mathcal{X}$ for every prime ideal $P$ of $D$. In this paper, we study the transfer of local properties of integral domains under several extensions and constructions, including flat overrings, Nagata ideal transforms, polynomial rings and their quotient extensions, and pullback constructions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_09565 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Local properties of integral domains under extensions and pullback constructions Baek, Hyungtae Lim, Jung Wook Ouzzaouit., Omar Tamoussit, Ali Commutative Algebra For a property $\mathcal{X}$ of integral domains, an integral domain $D$ is said to be a {\it locally $\mathcal{X}$-domain} if $D_P$ has the property $\mathcal{X}$ for every prime ideal $P$ of $D$. In this paper, we study the transfer of local properties of integral domains under several extensions and constructions, including flat overrings, Nagata ideal transforms, polynomial rings and their quotient extensions, and pullback constructions. |
| title | Local properties of integral domains under extensions and pullback constructions |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2601.09565 |