Introduction to Galois Theory

By Simone Malacrida

The following topics are presented in this book:
symmetric polynomials, symmetric functions, symmetric relations and Cauchy modules
Galois group and Galois theory of equations
binomial equations and fundamental theorem
inverse Galois problem and Ruffini-Abel theorem
resolutions of second, third, and fourth degree equations and monodromy

• Language: English
• Publisher: Simone Malacrida
• Release date: Dec 19, 2022
• ISBN: 9798215605387

Simone Malacrida

Simone Malacrida (1977) Ha lavorato nel settore della ricerca (ottica e nanotecnologie) e, in seguito, in quello industriale-impiantistico, in particolare nel Power, nell'Oil&Gas e nelle infrastrutture. E' interessato a problematiche finanziarie ed energetiche. Ha pubblicato un primo ciclo di 21 libri principali (10 divulgativi e didattici e 11 romanzi) + 91 manuali didattici derivati. Un secondo ciclo, sempre di 21 libri, è in corso di elaborazione e sviluppo.

Book preview

Introduction to Galois Theory

SIMONE MALACRIDA

The following topics are presented in this book:

symmetric polynomials, symmetric functions, symmetric relations and Cauchy modules

Galois group and Galois theory of equations

binomial equations and fundamental theorem

inverse Galois problem and Ruffini-Abel theorem

resolutions of second, third, and fourth degree equations and monodromy

Simone Malacrida (1977)

Engineer and writer, has worked on research, finance, energy policy and industrial plants.

ANALYTICAL INDEX

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INTRODUCTION

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I – BASIC CONCEPTS

Symmetric polynomials and Cauchy moduli

Symmetrical relationships

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II - GALOIS THEORY OF EQUATIONS

Galois group

Fundamental modules and reduction of the Galois group

Property of the Galois group

Extension for abelian groups and primitive groups

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III - APPLICATIONS OF THE GALOIS THEORY

Binomial equations

Solvability by radicals

Fundamental theorem

The inverse G alois problem

More results

Solving quadratic equations

Solving third degree equations

Solving quadratic equations

Ruffini-Abel theorem

Monodromy

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IV - TOPOLOGICAL VIEW OF THE GALOIS THEORY

Introduction and definitions

Results of the theory

INTRODUCTION

Galois theory is based on a different interpretation of the elementary algebraic equations and extends in a very general way results coming from disparate disciplines: from geometric ones such as the construction of regular polynomials with straightedge and compass to topological ones, going to define the very concepts of field and group up to complex analysis.

As such, its elaboration seemed a bit obscure in the history of mathematics, a sort of basic incomprehension concealed the ingenious revelations of Galois (which, we recall, by chance, were not