Notice bibliographique
- Notice
Type(s) de contenu et mode(s) de consultation : Texte noté : sans médiation
Auteur(s) : Garling, D. J. H. (1937-....)
Titre(s) : Galois theory and its algebraic background [Texte imprimé] / D.J.H. Garling,...
Édition : 2nd ed.
Publication : Cambridge : Cambridge university press, copyright 2022
Description matérielle : 1 vol.(X-195 p.) ; 23 cm
Note(s) : Index
"Galois theory, the theory of polynomial equations and their solutions, is one of
the most fascinating and beautiful subjects in pure mathematics. Using group theory
and field theory, it provides a complete answer to the problem of the solubility of
polynomial equations by radicals: that is, determining when and how a polynomial equation
can be solved by repeatedly extracting roots using elementary algebraic operations.
This textbook contains a fully detailed account of Galois theory and the algebra that
it needs and is suitable for both those following a course of lectures and the independent
reader (who is assumed to have no previous knowledge of Galois theory). This second
edition has been significantly revised and reordered; the first part develops the
basic algebra that is needed, and the second part gives a comprehensive account of
Galois theory. There are applications to ruler-and-compass constructions, and to the
solution of classical mathematical problems of ancient times. There are new exercises
throughout, and carefully selected examples will help the reader develop a clear understanding
of the mathematical theory"
Sujet(s) : Galois, Théorie de
Manuels d'enseignement supérieur
Indice(s) Dewey :
512.32 (23e éd.) = Théorie de Galois (mathématiques)
Identifiants, prix et caractéristiques : ISBN 978-1-108-96908-6 (br.)
Identifiant de la notice : ark:/12148/cb47128527c
Notice n° :
FRBNF47128527
(notice reprise d'un réservoir extérieur)
Table des matières : Groups ; Integral domains ; Vector spaces and determinants ; Field extensions
; Ruler and compass constructions ; Splitting fields ; Normal extensions ; Separability
; The fundamental theorem of Galois theory ; The discriminant ; Cyclotomic polynomials
and cyclic extensions ; Solution by radicals ; Regular polygons ; Polynomials of
low degree ; Finite fields ; Quintic polynomials ; Further theory ; The algebraic
closure of a field ; Transcendental elements and algebraic independence ; Generic
and symmetric polynomials.
