Abstract
The roots of polynomials over Cayley–Dickson algebras over an arbitrary field and of arbitrary dimension are studied. It is shown that the spherical roots of a polynomial f(x) are also roots of its companion polynomial . We generalize the classical theorems for complex and real polynomials by Gauss–Lucas and Jensen to locally-complex Cayley–Dickson algebras: it is proved that the spherical roots of belong to the convex hull of the roots of , and we also show that all roots of are contained in the snail of f(x), as defined by Ghiloni and Perotti.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have