Flipped non-associative polynomial rings and the Cayley-Dickson construction
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917772072583168 |
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| author | Aryapoor, Masood Bäck, Per |
| author_facet | Aryapoor, Masood Bäck, Per |
| contents | We introduce and study flipped non-associative polynomial rings. In particular, we show that all Cayley-Dickson algebras naturally appear as quotients of a certain type of such rings; this extends the classical construction of the complex numbers (and quaternions) as a quotient of a (skew) polynomial ring to the octonions, and beyond. We also extend some classical results on algebraic properties of Cayley-Dickson algebras by McCrimmon to a class of flipped non-associative polynomial rings. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_03763 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Flipped non-associative polynomial rings and the Cayley-Dickson construction Aryapoor, Masood Bäck, Per Rings and Algebras 16W10, 17A20, 17A35, 17A70, 17A75, 17D05 We introduce and study flipped non-associative polynomial rings. In particular, we show that all Cayley-Dickson algebras naturally appear as quotients of a certain type of such rings; this extends the classical construction of the complex numbers (and quaternions) as a quotient of a (skew) polynomial ring to the octonions, and beyond. We also extend some classical results on algebraic properties of Cayley-Dickson algebras by McCrimmon to a class of flipped non-associative polynomial rings. |
| title | Flipped non-associative polynomial rings and the Cayley-Dickson construction |
| topic | Rings and Algebras 16W10, 17A20, 17A35, 17A70, 17A75, 17D05 |
| url | https://arxiv.org/abs/2403.03763 |