Ideals of regular functions of a quaternionic variable
Copyright policy )Ideals of regular functions of a quaternionic variable
In this paper we prove that, for any $n\in \mathbb N$, the ideal generated by $n$ slice regular functions $f_1,\ldots,f_n$ 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
- New York University Italy
- University of Florence Italy
- Chapman University United States
30G35, Algebra, Ideals of regular functions, Mathematics - Complex Variables, FOS: Mathematics, Functions of a quaternionic variable, Complex Variables (math.CV), Functions of a quaternionic variable, Ideals of regular functions
30G35, Algebra, Ideals of regular functions, Mathematics - Complex Variables, FOS: Mathematics, Functions of a quaternionic variable, Complex Variables (math.CV), Functions of a quaternionic variable, Ideals of regular functions
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