Article
| Title: | Why quintic polynomial equations are not solvable in radicals (English) |
| Author: | Křížek, Michal |
| Author: | Somer, Lawrence |
| Language: | English |
| Journal: | Application of Mathematics 2015 |
| Volume: | Proceedings. Prague, November 18-21, 2015 |
| Issue: | 2015 |
| Year: | |
| Pages: | 125-131 |
| . | |
| Category: | math |
| . | |
| Summary: | We illustrate the main idea of Galois theory, by which roots of a polynomial equation of at least fifth degree with rational coefficients cannot general be expressed by radicals, i.e., by the operations $+,\,-,\,\cdot,\,:\,$, and $\root n \of{\cdot}$. Therefore, higher order polynomial equations are usually solved by approximate methods. They can also be solved algebraically by means of ultraradicals. (English) |
| Keyword: | Galois theory |
| Keyword: | finite group |
| Keyword: | permutation |
| Keyword: | radical |
| MSC: | 13B05 |
| MSC: | 20D05 |
| MSC: | 65H05 |
| idZBL: | Zbl 06669924 |
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| Date available: | 2017-02-14T10:24:06Z |
| Last updated: | 2017-03-20 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/702970 |
| . |
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| Files | Size | Format | View |
|---|---|---|---|
| ApplMath_03-2015-1_14.pdf | 227.3Kb | application/pdf |
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