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Einführung in Die Algebra by H. Lüneburg

Einführung in Die Algebra

by H. Lüneburg
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Book cover type: Paperback
  • ISBN13: 9783540062608
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Publication Date:
  • Pages: 292
  • Original Price: EUR 46.72
  • Language: German
  • Edition: N/A
  • Item Weight: 531 grams
  • BISAC Subject(s): Algebra / General

Die vorlie nden Blatter stellen bis auf r Abweich n den Inhalt einer drei- semestri n Anfan rvorlesung liber lineare AI bra dar, die ich vorn Winter 1970/71 bis zum Winter 1971/72 in Kaiserslautern hal ten habe. J'lEin Hauptanlie n bei dieser Vorlesung war, den etwas trockenen Stoff der linearen Algebra durch viele Beispiele und interessante Anwendun n reizvoller zu stalten und durch die Beispiele auch dern Man l ein wenig abzuhelfen, dern man immer wieder auch bei der ei nen Arbeit begegnet, daB es narnlich leichter fallt, einen Satz zu beweisen als ein Gegenbeispiel fUr eine Verrrn. ttung zu finden. Die meisten Beispiele dieses Buches sind Beispiele fUr Ringe und KBrper: Der Ring der ganzen Zahlen und seine homomorphen Bilder werden untersucht, die ganzen Hensel'schen p-adischen Zahlen werden als Endomorphismenri der PrUfergruppen konstruiert, die ihrerseits interessante Beispiele von Gruppen liefern, die, wie man weiB, in der 'Iheo- rie der abelschen Gruppen eine greBe Rolle spielen; die Hensel'schen p-adischen Zahlen erscheinen als Quotientenkorper dieser Ringe. Ferner werden aIle Galoisfelder konstru- iert und zeigt, daB dies alle endlichen Korper sind. Die Endomorphismenrin von Vektorraumen liefem eine weitere Klasse von interessanten Beispielen. Die Struktur ihrer Rechts- und Linksidealverbande wird eingehend untersucht. SchlieBlich wird zu jeder Charakteristik ein Quaternionenschiefkorper konstruiert und zur Charakteristik Null sogar abzablbar viele, paarweise nicht isornorphe. Die ganzen Gauf. >' schen Zahlen sind ein Beispiel fUr einen euklidischen-Ring und mit ihrer Hilfe und der Theorie der euklidischen Rin erhalt man einen Beweis fUr den Fermat'schen zwei-Quadrate-Satz.

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