A necessary condition for solvability by radicals
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908950568370176 |
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| author | Khovanskii, Askold |
| author_facet | Khovanskii, Askold |
| contents | This note was prepared as a handout for the MAT401 course ``Polynomial equations and fields", taught at the University of Toronto in Spring 2026. It presents a proof of a necessary condition for the solvability of algebraic equations by radicals, based on Galois theory. We begin with a brief overview of the relevant basic results from Galois theory, as covered in MAT401, and use -- without proof -- several standard (and relatively simple) results from the course textbook [1]. The sufficient condition for solvability by radicals, which is based on linear algebra, we will present in the next handout. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_08642 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A necessary condition for solvability by radicals Khovanskii, Askold Rings and Algebras This note was prepared as a handout for the MAT401 course ``Polynomial equations and fields", taught at the University of Toronto in Spring 2026. It presents a proof of a necessary condition for the solvability of algebraic equations by radicals, based on Galois theory. We begin with a brief overview of the relevant basic results from Galois theory, as covered in MAT401, and use -- without proof -- several standard (and relatively simple) results from the course textbook [1]. The sufficient condition for solvability by radicals, which is based on linear algebra, we will present in the next handout. |
| title | A necessary condition for solvability by radicals |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2604.08642 |