惊呼
发表于 2025-3-26 23:32:34
Airbreathing Hypersonic Propulsion show how to find similar formulae for cubic and quartic equations. We also explain why as early as the eighteenth century mathematicians started to doubt the possibility to find solutions for general quintic equations (or equations of higher degrees) using the four arithmetic operations and extract
Dri727
发表于 2025-3-27 02:04:39
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ALT
发表于 2025-3-27 05:35:30
https://doi.org/10.1007/978-3-662-02646-5 is a zero of a nontrivial polynomial with coefficients in K. We relate the elements of algebraic extensions to the corresponding polynomials and look at the structures of the simplest extensions .(.) of K. We also introduce the notion of the degree of a field extension and prove some of its propert
毕业典礼
发表于 2025-3-27 13:17:55
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debouch
发表于 2025-3-27 15:08:14
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熔岩
发表于 2025-3-27 18:39:37
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人充满活力
发表于 2025-3-28 01:58:43
https://doi.org/10.1007/978-3-658-33721-6d in most common situations). An extension of a field is separable if any irreducible polynomial with coefficients in this field does not have multiple zeros. All extensions of fields of characteristic zero and all finite extensions of finite fields have this property. For this reason, there are som
强壮
发表于 2025-3-28 05:26:55
https://doi.org/10.1007/978-1-349-02425-4alois extensions, i.e. the extensions which are both normal and separable. One of the most central results is Galois’ correspondence between the subgroups of the Galois group of such an extension and the intermediate subfields of it. In the exercises, we find many examples and interesting properties
Functional
发表于 2025-3-28 08:25:03
https://doi.org/10.1057/9781403920096ed by the roots of 1. Even if such fields are simple to describe in purely algebraic terms, they are rich as mathematical objects. We explore some of their properties, which find different applications in number theory and algebra. Among many applications, there is a proof of a special case of Diric
pessimism
发表于 2025-3-28 10:36:28
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