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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.12711 |
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| _version_ | 1866914921314254848 |
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| author | Motiee, Mehran |
| author_facet | Motiee, Mehran |
| contents | The first examples of noncrossed product division algebras were given by Amitsur in 1972. His method is based on two basic steps: (1) If the universal division algebra $U(k,n)$ is a $G$-crossed product then every division algebra of degree $n$ over $k$ should be a $G$-crossed product; (2) There are two division algebras over $k$ whose maximal subfields do not have a common Galois group. In this note, we give a short proof for the second step in the case where $\chr k\nmid n$ and $p^3|n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_12711 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A proof for a part of noncrossed product theorem Motiee, Mehran Rings and Algebras The first examples of noncrossed product division algebras were given by Amitsur in 1972. His method is based on two basic steps: (1) If the universal division algebra $U(k,n)$ is a $G$-crossed product then every division algebra of degree $n$ over $k$ should be a $G$-crossed product; (2) There are two division algebras over $k$ whose maximal subfields do not have a common Galois group. In this note, we give a short proof for the second step in the case where $\chr k\nmid n$ and $p^3|n$. |
| title | A proof for a part of noncrossed product theorem |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2408.12711 |