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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2019
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1903.00560 |
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| _version_ | 1866911366422462464 |
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| author | Chari, Sara Smertnig, Daniel Voight, John |
| author_facet | Chari, Sara Smertnig, Daniel Voight, John |
| contents | A quaternion order O over a Dedekind domain R is Bass if every R-superorder is Gorenstein, and O is basic if it contains an integrally closed quadratic R-order. In this article, we show that these conditions are equivalent in local and global settings: a quaternion order is Bass if and only if it is basic. In particular, we show that the property of being basic is a local property of a quaternion order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1903_00560 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | On basic and Bass quaternion orders Chari, Sara Smertnig, Daniel Voight, John Rings and Algebras A quaternion order O over a Dedekind domain R is Bass if every R-superorder is Gorenstein, and O is basic if it contains an integrally closed quadratic R-order. In this article, we show that these conditions are equivalent in local and global settings: a quaternion order is Bass if and only if it is basic. In particular, we show that the property of being basic is a local property of a quaternion order. |
| title | On basic and Bass quaternion orders |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/1903.00560 |