Roots and right factors of polynomials and left eigenvalues of matrices over Cayley-Dickson algebras

Adam Chapman, Solomon Vishkautsan

Over a composition algebra $A$, a polynomial $f(x)\in A[x]$ has a root $\alpha$ if and only $f(x)=g(x)\cdot (x-\alpha )$ for some $g(x)\in A[x]$. We examine whether this is true for general…