Abel's impossibility proof as reflected in modern Galois theory
type: Item
instance of: scholarly article
title: Abel's impossibility proof as reflected in modern Galois theory
zbMATH Open document ID: 0931.12001
author: Ivo Radloff
published in: Mathematische Semesterberichte
publication date: 1999-11-10T00:00:00Z
review text: In 1826, N. H. Abel proved that the general algebraic equation of degree \(n\) is not solvable by radicals for \(n > 4\). In the present paper, Abel's proof is reformulated and completed by using modern terminology and Galois theory. Otherwise, the present author follows closely Abel's original method. At the end he indicates that Abel's proof is basically correct, just a couple of theorems needing a more detailed treatment. Reviewer's remark: \textit{Lars Gårding} [Normat 40, No. 1, 1-13 (1992; Zbl 0769.12001)] has written a similar article about Abel's manuscript on soluble equations of prime degree.
Mathematics Subject Classification ID: 12-03
Mathematics Subject Classification ID: 01A55
Mathematics Subject Classification ID: 12F10
Mathematics Subject Classification ID: 12E05
zbMATH DE Number: 1337921
zbMATH Keywords: general algebraic equation
zbMATH Keywords: unsolvable equation
zbMATH Keywords: Abel's theorem
reviewed by: Veikko Ennola
MaRDI profile type: Publication
full work available at URL: s005910050041
OpenAlex ID: W2023704393
DOI: 10.1007/S005910050041
description: scientific article; zbMATH DE number 1337921