Ideals of Regular Functions of a Quaternionic Variable
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.
Gentili, G., Sarfatti, G., & Struppa, D.C. (2013). Ideals of regular functions of a quaternionic variable. Retrieved from http://web.math.unifi.it/users/sarfatti/ideals.pdf