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.
2008
259
895
902
G. GENTILI; D. STRUPPA; F. VLACCI
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/211071
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