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Algebra: Einführung in Die Galoistheorie
Paperback
Series: de Gruyter Studium
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ISBN13: 9783110290707
Publisher: de Gruyter
Published: Aug 19 2013
Pages: 331
Weight: 1.25
Height: 0.70 Width: 6.60 Depth: 9.40
Language: German
Dieses Lehrbuch bietet eine Einführung in die grundlegenden Methoden der Galoistheorie. Am Beispiel der Auflösbarkeit von Polynomgleichungen durch Radikale wird das Zusammenwirken dreier Theorien - Gruppentheorie, Körpertheorie und Ringtheorie - zur Lösung dieses Problems demonstriert. Behandelt werden neben den üblichen Grundbegriffen wie Gruppen, Körper und Ringe sowie den Resultaten der Galoistheorie auch Anwendungen auf Konstruktionen mit Zirkel und Lineal, endliche Körper und Kreisteilungskörper sowie Auflösungsformeln der Gleichungen vom Grad höchstens 4. Darüber hinaus wird der konkreten Berechenbarkeit und den Algorithmen zur Bestimmung irreduzibler Teiler von Polynomen bzw. der Galoisgruppe eines moderaten Polynoms ein breiter Raum gewidmet.
Die vorliegende zweite Auflage enthält Erweiterungen zu den Themen rein inseparable Körpererweiterungen, p-adische Zahlen und Bewertungstheorie, angeordnete Körper und Satz von Sturm.
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