A characterization of transfer Krull orders in Dedekind domains with torsion class group
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917388081954816 |
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| author | Rago, Balint |
| author_facet | Rago, Balint |
| contents | We establish a characterization (under some natural conditions) of those orders in Dedekind domains which allow a transfer homomorphism to a monoid of zero-sum sequences. As a consequence, the inclusion map to the Dedekind domain is a transfer homomorphism, with the exception of a particular case. The arithmetic of Krull and Dedekind domains is well understood, and the existence of a transfer homomorphism implies that the order and the associated Dedekind domain share the same arithmetic properties. This is not the case for arbitrary orders in Dedekind domains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_00271 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A characterization of transfer Krull orders in Dedekind domains with torsion class group Rago, Balint Commutative Algebra 11R27, 13A05, 13F05 We establish a characterization (under some natural conditions) of those orders in Dedekind domains which allow a transfer homomorphism to a monoid of zero-sum sequences. As a consequence, the inclusion map to the Dedekind domain is a transfer homomorphism, with the exception of a particular case. The arithmetic of Krull and Dedekind domains is well understood, and the existence of a transfer homomorphism implies that the order and the associated Dedekind domain share the same arithmetic properties. This is not the case for arbitrary orders in Dedekind domains. |
| title | A characterization of transfer Krull orders in Dedekind domains with torsion class group |
| topic | Commutative Algebra 11R27, 13A05, 13F05 |
| url | https://arxiv.org/abs/2411.00271 |