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On the structure of the set of zeros of quaternionic polynomials. (English) Zbl 1160.30353
Summary: We prove that any quaternionic polynomial (with the coefficients on the same side) has two types of zeros: the zeros are either isolated or spherical ones, i.e., those ones which form a whole sphere. What is more, the total quantity of the isolated zeros and of the double number of the spheres does not outnumber the degree of the polynomial.

MSC:
30G35 Functions of hypercomplex variables and generalized variables
12E12 Equations in general fields
16H05 Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.)
11R52 Quaternion and other division algebras: arithmetic, zeta functions
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