The fundamental theorem of algebra for Hamilton and Cayley numbers

DOI10.1007/s00209-007-0254-9zbMath1144.30004OpenAlexW1986006810MaRDI QIDQ930504

Graziano Gentili, Fabio Vlacci, Daniele C. Struppa

Publication date: 30 June 2008

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00209-007-0254-9

Mathematics Subject Classification ID

Functions of hypercomplex variables and generalized variables (30G35) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Other generalizations of function theory of one complex variable (32A30)

Related Items (24)

Newton method in the context of quaternion analysis ⋮ Slice-polynomial functions and twistor geometry of ruled surfaces in \(\mathbb {CP}^3\) ⋮ Slice regular functions on real alternative algebras ⋮ Solution of a quadratic quaternion equation with mixed coefficients ⋮ Zero sets and Nullstellensatz type theorems for slice regular quaternionic polynomials ⋮ Vieta's formulae for regular polynomials of a quaternionic variable ⋮ Scalar-vector algorithm for the roots of quadratic quaternion polynomials, and the characterization of quintic rational rotation-minimizing frame curves ⋮ Complex Roots of Quaternion Polynomials ⋮ Zeros of regular functions of quaternionic and octonionic variable: a division lemma and the camshaft effect ⋮ The Weierstrass factorization theorem for slice regular functions over the quaternions ⋮ Lower bounds for polynomials of a quaternionic variable ⋮ Twistor transforms of quaternionic functions and orthogonal complex structures ⋮ The Bohr Theorem for slice regular functions ⋮ A central quaternionic Nullstellensatz ⋮ Regular Moebius transformations of the space of quaternions ⋮ Factoring skew polynomials over Hamilton's quaternion algebra and the complex numbers ⋮ A new method for roots of monic quaternionic quadratic polynomial ⋮ The classification and the computation of the zeros of quaternionic, two-sided polynomials ⋮ Polynomials and degrees of maps in real normed algebras ⋮ Zeros of regular functions and polynomials of a quaternionic variable ⋮ Rigidity for regular functions over Hamilton and Cayley numbers and a boundary Schwarz' lemma ⋮ Quaternionic-valued ordinary differential equations. The Riccati equation ⋮ Computations in the ring of quaternionic polynomials ⋮ Roots of quaternion polynomials: theory and computation

Cites Work

• Unnamed Item
• Unnamed Item
• A new theory of regular functions of a quaternionic variable
• A new approach to Cullen-regular functions of a quaternionic variable
• Differential Topology
• Quaternionic analysis
• The octonions
• On the Structure of the Set of Zeros of Quaternionic Polynomials
• Equations in Quaternions
• The Roots of a Quaternion
• The “fundamental theorem of algebra” for quaternions

This page was built for publication: The fundamental theorem of algebra for Hamilton and Cayley numbers