Galois Theory

Askold Khovanskii
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Askold Khovanskii: University of Toronto, Dept. Mathematics

Chapter Chapter 1 in Galois Theory, Coverings, and Riemann Surfaces, 2013, pp 1-40 from Springer

Abstract: Abstract The first chapter is an exposition of Galois theory and its applications to the questions of solvability of algebraic equations in explicit form. Apart from the classical problem on solvability of an algebraic equation by radicals, we also consider other problems of this type, for instance, the question of solvability of an equation by radicals and by solving auxiliary equations of degree at most k. While our proof of the fundamental theorem of Galois theory is valid for infinite fields we also check explicitly that the fundamental theorem holds for finite fields.

Keywords: Galois Theory; Invariant Subfield; Lagrange Resolvents; Galois Equivalence; Galois Group (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-38841-5_1

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DOI: 10.1007/978-3-642-38841-5_1

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