Abstract. In this paper we prove the fundamental theorem of algebra for polynomials with coefficients in the skew field of Hamilton numbers (quaternions) and in the division algebra of Cayley numbers (octonions). The proof, inspired by recent definitions and results on regular functions of a quaternionic and of a octonionic variable, follows the guidelines of the classical topological argument due to Gauss.
The Fundamental Theorem of Algebra for Hamilton and Cayley numbers / G. GENTILI; D. STRUPPA; F. VLACCI. - In: MATHEMATISCHE ZEITSCHRIFT. - ISSN 0025-5874. - STAMPA. - 259:(2008), pp. 895-902. [10.1007/s00209-007-0254-9]
The Fundamental Theorem of Algebra for Hamilton and Cayley numbers
GENTILI, GRAZIANO;VLACCI, FABIO
2008
Abstract
Abstract. In this paper we prove the fundamental theorem of algebra for polynomials with coefficients in the skew field of Hamilton numbers (quaternions) and in the division algebra of Cayley numbers (octonions). The proof, inspired by recent definitions and results on regular functions of a quaternionic and of a octonionic variable, follows the guidelines of the classical topological argument due to Gauss.File | Dimensione | Formato | |
---|---|---|---|
PaperGSV7.pdf
Accesso chiuso
Tipologia:
Versione finale referata (Postprint, Accepted manuscript)
Licenza:
Tutti i diritti riservati
Dimensione
166.25 kB
Formato
Adobe PDF
|
166.25 kB | Adobe PDF | Richiedi una copia |
I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.