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 |
