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Über Kriterien für irreduzible und für primitive Gleichungen und über die Aufstellung affektfreier Gleichungen

In: Festschrift

Author

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  • Ph. Furtwängler

Abstract

Zusammenfassung Eines der brauchbarsten Kriterien für die Irreduzibilität algebraischer Gleichungen ist das Eisensteinsche. Die folgenden Entwicklungen enthalten implizite einen neuen Beweis dieses Kriteriums, der mir deshalb bemerkenswert zu sein scheint, weil er sehr leicht zu Verallgemeinerungen führt (§ 1 und 2). Es läßt sich insbesondere auch auf diesem Wege ein Kriterium für primitive Gleichungen herleiten (§ 3). Ich verwende schließlich die gefundenen Kriterien, um in einfachster Weise affektfreie Gleichungen beliebigen Grades 1) aufzustellen, indem ich die Tatsache benutze, daß irreduzible primitive Gleichungen beliebigen Grades mit genau zwei komplexen Wurzeln affektfrei sind (§ 4).

Suggested Citation

  • Ph. Furtwängler, 1982. "Über Kriterien für irreduzible und für primitive Gleichungen und über die Aufstellung affektfreier Gleichungen," Springer Books, in: Festschrift, pages 34-40, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-61810-9_5
    DOI: 10.1007/978-3-642-61810-9_5
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