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Allgemeine Algebra Und Anwendungen by Phil Dietmar W. Dorninger, Phil Winfried B. Müller

Allgemeine Algebra Und Anwendungen

by Phil Dietmar W. Dorninger , Phil Winfried B. Müller
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Book cover type: Paperback
  • ISBN13: 9783519020301
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Vieweg+teubner Verlag
  • Publisher Imprint: Vieweg+teubner Verlag
  • Publication Date:
  • Pages: 328
  • Original Price: EUR 46.72
  • Language: German
  • Edition: Softcover Repri
  • Item Weight: 468 grams
  • BISAC Subject(s): Engineering (General)

Ausgehend von dem Werk des Arabers Mohammed ibn Musa al-Khowarizmi "Hisab aljabr w'almuqabalah" (HinUberschaffen eines Gliedes einer Gleichung von einer Seite auf die andere) im 8. Jhdt. nach ehr., welches fUr die Algebra namensgebend war, verstand man bis zum Beginn des 19. Jhdts. unter Algebra im wesentlichen die Lehre von der Lösung alge- braischer Gleichungen . Eines der Hauptprobleme der Gleichungslehre war, die Frage zu beantworten, wann eine allgemeine Polynomgleichung n-ten Grades mit Hilfe der Grundrechnungsarten, des Potenzierens und Wurzel- ziehens auflösbar ist. Diese Frage wurde von E. Galois in einer im Jahre 1831 bei der Französischen Akademie der Wissenschaften einge- reichten Arbeit endgUltig entschieden. Galois verwendete bei seinem Be- weis erstmals Hilfsmittel, die als charakteristisch fUr die moderne Al- gebra angesehen werden können, nämlich Eigenschaften von Gruppen und Körpern . - Angeregt durch Fragen der Logik folgten bald Untersuchungen anderer algebraischer Strukturen, nämlich von Booleschen Algebren, und mit der Zeit wandelte sich die Bedeutung des Wortes Algebra hin zur Lehre von algebraischen Strukturen, so wie wir sie heute vornehml ich verstehen. Mit den vielen neu gewonnenen Ergebnissen Uber algebraische Strukturen gewann die Frage an Bedeutung, was diesen Ergebnissen gemeinsam ist, und so entstand vor etwa 30 Jahren eine neue Teildisziplin der Algebra, die sogenannte Universelle (oder Universale) Algebra. Zugleich mit dem Trend zur abstrakten Algebra hin geriet allerdings teilweise etwas in Ver- gessenheit, da viele Probleme der Algebra aus konkret en Fragen der An- wendungen entstanden und fUr die Anwendungen bedeutsam sind.

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