Ideals of Regular Functions of a Quaternionic Variable

Document Type


Publication Date



In this paper we prove that, for any n∈ N, the ideal generated by n slice regular functions f1,..., fn 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.


This is the pre-print of an article that will be published at a later date. This version has not yet undergone peer review and may differ from the final, published version.