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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.14485 |
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| _version_ | 1866915951243427840 |
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| author | Lorenz, Nico Schönert, Alexander |
| author_facet | Lorenz, Nico Schönert, Alexander |
| contents | We present a new approach to verify the Elementary Type Conjecture for abstract Witt rings with small number of square classes. To do so, we make use of an abstract analogue of the 2-torsion part of the Brauer group, also verifying a certain case of the Arason-Pfister Hauptsatz in this setting. We develop a description of the entire structure of an abstract Witt ring with $2^n$ square classes in terms of a unique $n\times n$ matrix. Via computational search, we find all these matrices for $n$ up to $7$. All obtained results affirm the Elementary Type Conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_14485 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Normal Quaternionic Matrices and Finitely Generated Witt Rings Lorenz, Nico Schönert, Alexander Rings and Algebras 11E81, 16K50 We present a new approach to verify the Elementary Type Conjecture for abstract Witt rings with small number of square classes. To do so, we make use of an abstract analogue of the 2-torsion part of the Brauer group, also verifying a certain case of the Arason-Pfister Hauptsatz in this setting. We develop a description of the entire structure of an abstract Witt ring with $2^n$ square classes in terms of a unique $n\times n$ matrix. Via computational search, we find all these matrices for $n$ up to $7$. All obtained results affirm the Elementary Type Conjecture. |
| title | Normal Quaternionic Matrices and Finitely Generated Witt Rings |
| topic | Rings and Algebras 11E81, 16K50 |
| url | https://arxiv.org/abs/2505.14485 |