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Galois theory: Abel's theorem
Автор: Richard E Borcherds
Загружено: 2021-01-08
Просмотров: 11863
Описание:
This lecture is part of an online graduate course on Galois theory.
We discuss Abel's theorem, that says a general quintic equation cannot be solved by radicals. We do this by showing that if a polynomial can be solved by radicals over a field of characteristic 0 then its roots lie in a solvable Galois extension. We give some examples of degree 5 polynoimals whose roots do not generate a solvable extension.
The results about group theory used in the lecture are discussed in the group theory course • Group theory
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