Verfasst von: | Garling, David J. H. [VerfasserIn] |
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 |
K10plus-PPN: | 1750508486 |
978-1-108-83892-4,978-1-108-96908-6
Galois theory and its algebraic background / Garling, David J. H. [VerfasserIn]; 2022
68774206