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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.11154 |
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| _version_ | 1866909139317293056 |
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| author | Chapman, Adam |
| author_facet | Chapman, Adam |
| contents | We prove that two cyclically linked $p$-algebras of prime degree become inseparably linked under a prime to $p$ extension if and only if the essential $p$-dimension of the pair is 2. We conclude that the essential $p$-dimension of pairs of cyclically linked $p$-algebras is 3 by constructing an example of a pair that does not become inseparably linked under any prime to $p$ extension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_11154 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Linkage and Essential $p$-Dimension Chapman, Adam Rings and Algebras 16K20 (primary), 13A35, 19D45 (secondary) We prove that two cyclically linked $p$-algebras of prime degree become inseparably linked under a prime to $p$ extension if and only if the essential $p$-dimension of the pair is 2. We conclude that the essential $p$-dimension of pairs of cyclically linked $p$-algebras is 3 by constructing an example of a pair that does not become inseparably linked under any prime to $p$ extension. |
| title | Linkage and Essential $p$-Dimension |
| topic | Rings and Algebras 16K20 (primary), 13A35, 19D45 (secondary) |
| url | https://arxiv.org/abs/2403.11154 |