Mathematical Research Letters

Volume 23 (2016)

Number 6

Ideals of regular functions of a quaternionic variable

Pages: 1645 – 1663

DOI: https://dx.doi.org/10.4310/MRL.2016.v23.n6.a4

Authors

Graziano Gentili (Dipartimento di Matematica e Informatica, Università di Firenze, Italy)

Giulia Sarfatti (Dipartimento di Matematica e Informatica, Università di Firenze, Italy)

Daniele C. Struppa (Schmid College of Science & Technology, Chapman University, Orange, California, U.S.A.)

Abstract

In this paper we prove that, for any $n \in \mathbb{N}$, the ideal generated by $n$ slice regular functions $f_1, \dotso , f_n$ having no common zeroes coincides 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.

Keywords

functions of a quaternionic variable, Ideals of regular functions

2010 Mathematics Subject Classification

30G35

Full Text (PDF format)

Accepted 25 April 2015

Published 21 February 2017