Ideals of regular functions of a quaternionic variable

2016/11/27 by Graziano Gentili, Giulia Sarfatti, Gentili, Graziano +3
Mathematics · #30G35 #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.1611.08827

openalex publication_date 2016/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we prove that, for any n∈ \mathbb N, the ideal generated by n slice regular functions f₁,…,f_n having no common zeros concides with the entire ring of slice regular functions. The proof required the study of the non-commutative syzygies of a vector of regular functions, that manifest a different character when compared with their complex counterparts.

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