Euclidean domains with no multiplicative norms
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
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| _version_ | 1866929748303675392 |
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| author | Dastrup, Caleb J. Nielsen, Pace P. |
| author_facet | Dastrup, Caleb J. Nielsen, Pace P. |
| contents | We construct a Euclidean domain with no multiplicative Euclidean norm to a compatibly well-ordered monoid, and hence with no multiplicative Euclidean norm to $\mathbb{R}$ (under its usual order).
A key step in the proof is showing that the UFD property is preserved when adjoining a free factorization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_05573 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Euclidean domains with no multiplicative norms Dastrup, Caleb J. Nielsen, Pace P. Commutative Algebra Rings and Algebras We construct a Euclidean domain with no multiplicative Euclidean norm to a compatibly well-ordered monoid, and hence with no multiplicative Euclidean norm to $\mathbb{R}$ (under its usual order). A key step in the proof is showing that the UFD property is preserved when adjoining a free factorization. |
| title | Euclidean domains with no multiplicative norms |
| topic | Commutative Algebra Rings and Algebras |
| url | https://arxiv.org/abs/2501.05573 |