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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/2508.07451 |
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| _version_ | 1866914230685401088 |
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| author | Chapman, Adam Levin, Ilan Zaninelli, Marco |
| author_facet | Chapman, Adam Levin, Ilan Zaninelli, Marco |
| contents | A division ring $D$ is Amitsur-Small if for every $n$ and every maximal left ideal $I$ in $D[x_1,\dots,x_n]$, $I \cap D[x_1,\dots,x_{n-1}]$ is maximal in $D[x_1,\dots,x_{n-1}]$. The goal of this note is to prove that cyclic division algebras of odd prime degree over their center are never Amitsur-Small. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_07451 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cyclic Division Algebras of Odd Prime Degree are never Amitsur-Small Chapman, Adam Levin, Ilan Zaninelli, Marco Rings and Algebras Algebraic Geometry 16K20, 16D25 A division ring $D$ is Amitsur-Small if for every $n$ and every maximal left ideal $I$ in $D[x_1,\dots,x_n]$, $I \cap D[x_1,\dots,x_{n-1}]$ is maximal in $D[x_1,\dots,x_{n-1}]$. The goal of this note is to prove that cyclic division algebras of odd prime degree over their center are never Amitsur-Small. |
| title | Cyclic Division Algebras of Odd Prime Degree are never Amitsur-Small |
| topic | Rings and Algebras Algebraic Geometry 16K20, 16D25 |
| url | https://arxiv.org/abs/2508.07451 |