Noncatenary Unique Factorization Domains
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911784133197824 |
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| author | Bonat, Alexandra Loepp, S. |
| author_facet | Bonat, Alexandra Loepp, S. |
| contents | We demonstrate a class of local (Noetherian) unique factorization domains (UFDs) that are noncatenary at infinitely many places. In particular, if $A$ is in our class of UFDs, then the prime spectrum of $A$ contains infinitely many disjoint (except at the maximal ideal) noncatenary subsets. As a consequence of our result, there are infinitely many height one prime ideals $P$ of $A$ such that $A/P$ is not catenary. We also construct a countable local UFD $A$ satisfying the property that for every height one prime ideal $P$ of $A$, $A/P$ is not catenary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_16549 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Noncatenary Unique Factorization Domains Bonat, Alexandra Loepp, S. Commutative Algebra 13J10, 13F15 We demonstrate a class of local (Noetherian) unique factorization domains (UFDs) that are noncatenary at infinitely many places. In particular, if $A$ is in our class of UFDs, then the prime spectrum of $A$ contains infinitely many disjoint (except at the maximal ideal) noncatenary subsets. As a consequence of our result, there are infinitely many height one prime ideals $P$ of $A$ such that $A/P$ is not catenary. We also construct a countable local UFD $A$ satisfying the property that for every height one prime ideal $P$ of $A$, $A/P$ is not catenary. |
| title | Noncatenary Unique Factorization Domains |
| topic | Commutative Algebra 13J10, 13F15 |
| url | https://arxiv.org/abs/2402.16549 |