On Roots of Polynomials over F[X]/ 〈p〉
This is the first part of a four-article series containing a Mizar [3], [1], [2] formalization of Kronecker’s construction about roots of polynomials in field extensions, i.e. that for every field F and every polynomial p ∈ F [X]\F there exists a field extension E of F such that p has a root over E....
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| Format: | Article |
| Language: | English |
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Sciendo
2019-07-01
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| Series: | Formalized Mathematics |
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| Online Access: | https://doi.org/10.2478/forma-2019-0010 |
| Summary: | This is the first part of a four-article series containing a Mizar [3], [1], [2] formalization of Kronecker’s construction about roots of polynomials in field extensions, i.e. that for every field F and every polynomial p ∈ F [X]\F there exists a field extension E of F such that p has a root over E. The formalization follows Kronecker’s classical proof using F [X]/<p> as the desired field extension E [9], [4], [6]. |
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| ISSN: | 1426-2630 1898-9934 |