On the Structure of the Set of Zeros of Quaternionic Polynomials

Abstract

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