NDLI: On the Multiplicity of Zeroes of Polynomials with Quaternionic Coefficients

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Fuzzy Fractional Monodromy and the Section–Hyperboloid

On the Multiplicity of Zeroes of Polynomials with Quaternionic Coefficients

Representation Formulae for Solutions to Some Classes of Higher Order Systems and Related Liouville Theorems

Combinatorial and Geometric Methods in Topology

Néron Models and Formal Groups

A Survey of Total Positivity

Degenerations of Representations of Associative Algebras

Motivic Homotopy Theory

Cluster Categories and Their Relation to Cluster Algebras and Semi-invariants

Aspects of Potential Theory on Manifolds, Linear and Non-linear

On Schrödinger-Poisson Systems

Normal Currents: Structure, Duality Pairings and div–curl Lemmas

On a q-Central Limit Theorem Consistent with Nonextensive Statistical Mechanics

Lectures on the Orbital Stability of Standing Waves and Application to the Nonlinear Schrödinger Equation

Moduli Stacks of Permutation Classes of Pointed Stable Curves

Singular Integrals and Potential Theory (II)

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On the Multiplicity of Zeroes of Polynomials with Quaternionic Coefficients

Content Provider	Springer Nature Link
Author	Gentili, Grazia Struppa, Daniele C.
Copyright Year	2008
Abstract	Regular polynomials with quaternionic coefficients admit only isolated zeroes and spherical zeroes. In this paper we prove a factorization theorem for such polynomials. Specifically, we show that every regular polynomial can be written as a product of degree one binomials and special second degree polynomials with real coefficients. The degree one binomials are determined (but not uniquely) by the knowledge of the isolated zeroes of the original polynomial, while the second degree factors are uniquely determined by the spherical zeroes. We also show that the number of zeroes of a polynomial, counted with their multiplicity as defined in this paper, equals the degree of the polynomial. While some of these results are known in the general setting of an arbitrary division ring, our proofs are based on the theory of regular functions of a quaternionic variable, and as such they are elementary in nature and offer explicit constructions in the quaternionic setting.
Starting Page	15
Ending Page	25
Page Count	11
File Format	PDF
ISSN	14249286
Journal	Milan Journal of Mathematics
Volume Number	76
Issue Number	1
e-ISSN	14249294
Language	English
Publisher	Birkhäuser-Verlag
Publisher Date	2008-01-01
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Mathematics Analysis
Content Type	Text
Resource Type	Article
Subject	Mathematics

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