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Signatur: UBN/SK 200 G233(2)   QR-Code
Standort: Zweigstelle Neuenheim / Freihandbereich Monograph  3D-Plan
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Verfasst von:Garling, David J. H. [VerfasserIn]   i
Titel:Galois theory and its algebraic background
Werktitel:Course in Galois theory
Verf.angabe:D.J.H. Garling, University of Cambridge
Ausgabe:Second edition
Verlagsort:Cambridge ; New York, NY
Verlag:Cambridge University Press
Jahr:2022
Umfang:x, 195 Seiten
Illustrationen:Illustrationen
Fussnoten:First edition published as Course in Galois theory, Cambridge University Press, 1986 ; Includes bibliographical references and index
ISBN:978-1-108-83892-4
 978-1-108-96908-6
Abstract: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.
 "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"--
DOI:doi:10.1017/9781108979184
URL:https://zbmath.org/?q=an%3A7298510
 DOI: https://doi.org/10.1017/9781108979184
Sprache:eng
Bibliogr. Hinweis:Erscheint auch als : Online-Ausgabe: Garling, D. J. H: Galois theory, and its algebraic background. - Cambridge ; New York, NY : Cambridge University Press, 2021 |(DLC)2021002527
RVK-Notation:SK 200   i
K10plus-PPN:1750508486
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UBN/SK 200 G233(2)QR-CodeZweigstelle Neuenheim / Freihandbereich Monographien3D-Planbestellbar
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