Splitting quaternion algebras defined over a finite field extension
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2019
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| _version_ | 1866916105574940672 |
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| author | Becher, Karim Johannes Bingöl, Fatma Kader Leep, David B. |
| author_facet | Becher, Karim Johannes Bingöl, Fatma Kader Leep, David B. |
| contents | We study systems of quadratic forms over fields and their isotropy over 2-extensions. We apply this to obtain particular splitting fields for quaternion algebras defined over a finite field extension. As a consequence, we obtain that every central simple algebra of degree 16 is split by a 2-extension of degree at most 2^{16}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1910_01868 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Splitting quaternion algebras defined over a finite field extension Becher, Karim Johannes Bingöl, Fatma Kader Leep, David B. Rings and Algebras 12E15, 16K20 We study systems of quadratic forms over fields and their isotropy over 2-extensions. We apply this to obtain particular splitting fields for quaternion algebras defined over a finite field extension. As a consequence, we obtain that every central simple algebra of degree 16 is split by a 2-extension of degree at most 2^{16}. |
| title | Splitting quaternion algebras defined over a finite field extension |
| topic | Rings and Algebras 12E15, 16K20 |
| url | https://arxiv.org/abs/1910.01868 |