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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.

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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