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| Natura: | Preprint |
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2025
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| Accesso online: | https://arxiv.org/abs/2503.17701 |
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| _version_ | 1866917965000081408 |
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| author | Diaz-Toca, Gema M. Lombardi, Henri Quitté, Claude |
| author_facet | Diaz-Toca, Gema M. Lombardi, Henri Quitté, Claude |
| contents | This note aims to construct an ``intrinsic'' splitting field for the polynomial $Y^n-1$ over the rational field $\bf Q$, in a way that Gauss, Kummer, Kronecker and Bishop would have liked. Contrary to the usual presentations, our construction does not use any splitting field of $Y^n-1$ which would be given before demonstrating the irreducibility of the cyclotomic polynomial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_17701 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cyclotomic polynomials without using the zeros of $Y^n-1$ Diaz-Toca, Gema M. Lombardi, Henri Quitté, Claude Number Theory Commutative Algebra This note aims to construct an ``intrinsic'' splitting field for the polynomial $Y^n-1$ over the rational field $\bf Q$, in a way that Gauss, Kummer, Kronecker and Bishop would have liked. Contrary to the usual presentations, our construction does not use any splitting field of $Y^n-1$ which would be given before demonstrating the irreducibility of the cyclotomic polynomial. |
| title | Cyclotomic polynomials without using the zeros of $Y^n-1$ |
| topic | Number Theory Commutative Algebra |
| url | https://arxiv.org/abs/2503.17701 |