Quaternionen und andere Zahlbereiche. Was kommt nach den komplexen Zahlen?

Name: Quaternionen und andere Zahlbereiche. Was kommt nach den komplexen Zahlen?
Brand: Atlantic Books
SKU: 9783656571308
Price: 4117.0 INR
Availability: InStock

by Bastian Vincken

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ISBN13: 9783656571308
Binding: Paperback
Subject: N/A
Publisher: Grin Verlag
Publisher Imprint: Grin Verlag
Publication Date: February 8, 2014
Pages: 98
Original Price: USD 48.9
Language: German
Edition: N/A
Item Weight: 137 grams
BISAC Subject(s): Number Theory

About The Book

Examensarbeit aus dem Jahr 2004 im Fachbereich Mathematik - Zahlentheorie, Note: 1,3, Rheinisch-Westfälische Technische Hochschule Aachen (Lehrstuhl A für Mathematik), Sprache: Deutsch, Abstract: Das traditionelle Zahlensystem gilt als wichtigste Grundlage in der Mathematik. Der Aufbau dieses Zahlensystems beginnt seit dem Ende des 19. Jahrhunderts bei den natürlichen Zahlen. Diese werden dann schrittweise zu den ganzen, den rationalen, den reellen bis hin zu den komplexen Zahlen erweitert. Die Schulmathematik umfasst im besten Fall das Zahlensystem bis hin zu den komplexen Zahlen. In dieser Arbeit wollen wir uns mit der Frage beschäftigen, ob es jenseits der komplexen Zahlen noch andere Zahlbereiche zu konstruieren gibt und inwieweit diese noch sinnvoll sind. Diese hyperkomplexen Zahlbereiche werden seit Beginn des 20. Jahrhunderts reelle Algebren genannt. Möchte man sich analog zu den komplexen Zahlen, die einen zweidimensionalen reellen Vektorraum bilden, höherdimensionale reelle Vektorräume zu hyperkomplexen Zahlbereichen machen, muss man entweder die Endlichkeit der Dimension aufgeben oder aber auf vertraute Körperaxiome wie die der Kommutativität oder der Assoziativität oder gar auf die Möglichkeit der Division verzichten. In dieser Arbeit werden wir uns auf die endlichdimensionalen Divisionsalgebren beschränken. Dies bedeutet, dass wir an der Endlichkeit der Dimension und der Möglichkeit der Division festhalten werden. Sollten wir diese Eigenschaften aufgeben, so würden wir von einer Masse neuer Zahlbereiche erschlagen werden. Diese neuen Zahlbereiche werden Eigenschaften aufweisen, die uns auf den ersten Blick merkwürdig vorkommen. Der _Vollständigkeitssatz_ der reellen Zahlen beinhaltet vomWort her schon eine gewisse _Vollständigkeit_ des Zahlbereichs. Wir werden feststellen, dass, je weiter man sich von den reellen Zahlen entfernt, immer mehr uns vertraute Eigenschaften verloren gehen und in diesem Zusammenhang deutlich machen, welche Kuriositäten mit de

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