6 research outputs found
Polynomials over quaternions and coquaternions: a unified approach
This paper aims to present, in a unified manner, results which are valid on both the algebras of quaternions and coquaternions and, simultaneously, call the attention to the main differences between these two algebras. The rings of one-sided polynomials over each of these algebras are studied and some important differences in what concerns the structure of the set of their zeros are remarked. Examples illustrating this different behavior of the zero-sets of quaternionic and coquaternionic polynomials are also presented.(undefined)info:eu-repo/semantics/publishedVersio
Zeros of regular functions of quaternionic and octonionic variable: a division lemma and the camshaft effect
We study in detail the zero set of a regular function of a quaternionic or
octonionic variable. By means of a division lemma for convergent power series,
we find the exact relation existing between the zeros of two octonionic regular
functions and those of their product. In the case of octonionic polynomials, we
get a strong form of the fundamental theorem of algebra. We prove that the sum
of the multiplicities of zeros equals the degree of the polynomial and obtain a
factorization in linear polynomials.Comment: Proof of Lemma 7 rewritten (thanks to an anonymous reviewer