Ideals of regular functions of a quaternionic variable

Abstract

In this paper we prove that, for any $n\in \mathbb{N}$, the ideal generated by $n$ slice regular functions $f_1,\dots ,f_n$ 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.

13 pages

References in corpus (1)

• A Bloch-Landau Theorem for slice regular functions