In this paper we prove that, for any natural number n, the ideal generated by n slice regular functions f_1 , . . . , 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.
Ideals of regular functions of a quaternionic variable / Gentili, Graziano; Sarfatti, Giulia; Struppa, Daniele C.. - In: MATHEMATICAL RESEARCH LETTERS. - ISSN 1073-2780. - STAMPA. - 23:(2016), pp. 1645-1663. [10.4310/MRL.2016.v23.n6.a4]
Ideals of regular functions of a quaternionic variable
SARFATTI, GIULIA;
2016-01-01
Abstract
In this paper we prove that, for any natural number n, the ideal generated by n slice regular functions f_1 , . . . , 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.File in questo prodotto:
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