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Resultants of slice regular polynomials in two quaternionic variables

Anna Gori, Giulia Sarfatti, Fabio Vlacci

Abstract

We introduce a non-commutative resultant, for slice regular polynomials in two quaternionic variables, defined in terms of a suitable Dieudonné determinant.We use this tool to investigate the existence of common zeros of slice regular polynomials.

Resultants of slice regular polynomials in two quaternionic variables

Abstract

We introduce a non-commutative resultant, for slice regular polynomials in two quaternionic variables, defined in terms of a suitable Dieudonné determinant.We use this tool to investigate the existence of common zeros of slice regular polynomials.
Paper Structure (5 sections, 21 theorems, 66 equations)

This paper contains 5 sections, 21 theorems, 66 equations.

Table of Contents

  1. Introduction
  2. Introduction to quaternionic slice regular functions
  3. Several variable case
  4. Preliminaries on non commutative determinants
  5. Non commutative Resultant

Key Result

Theorem 1

Given two slice regular polynomials $P,Q$ in two quaternionic variables, both their regular resultants belong to the right ideal generated by $P$ and $Q$.

Theorems & Definitions (45)

  • Theorem
  • Proposition
  • Proposition
  • Proposition
  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Theorem 2.4
  • Theorem 2.5: Identity Principle
  • Definition 2.6
  • ...and 35 more