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The fundamental theorem of algebra for Hamilton and Cayley numbers. (English) Zbl 1144.30004
Authors’ summary: 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.

30C15 Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral)
30G35 Functions of hypercomplex variables and generalized variables
32A30 Other generalizations of function theory of one complex variable (should also be assigned at least one classification number from Section 30-XX)
Full Text: DOI
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