… to be the polynomial ring over the octonions: the notion of an … of an octonionic polynomial by
a characteristic polynomial. … of an octonionic polynomial by a characteristic polynomial. From …

… We provide an analogue of Wedderburn’s factorization method for central polynomials
with coefficients in an octonion division algebra, and present an algorithm for fully factoring�…

… that if f(x) is a quadratic monic polynomial over an octonion division algebra and f(α) = α, …
for all polynomials over associative division algebras but false over octonion division algebras …

… We shall see that triality is a restriction of a polynomial mapping Cl8 → Cl8, of degree 2. We
will learn how to compose trialities, when they correspond to different octonion products. We …

… octonionic theories. Then, we introduce sundamental properties of what we call ordered
polynomials … but this is impossible by unique factorization of polynomials over Q. This proves …

… octonions, and consider their various applications to octonions as well as matrices of octonions…
Through the characteristic polynomial (2.24), one can also retern Eqs.(3.15) and (3.16) to …

In this project we describe the non-associative finite-dimensional composition algebra called
the Octonions and denoted O. We begin by introducing the structure and then go on to …

… In a small size finite field Fq, a univariate polynomial equation can be solved … factoring
polynomials over finite fields (see [14] for a survey) could be used to solve univariate polynomial …

… attacked and broken due to the factorization problem [11]. … algebras as well as the polynomial
quaternion algebra (ie, Q-… GGH using the octonion algebra and polynomial rings, which …

… of some of our results for the case of polynomials. Certain algebraic aspects of these proofs
… octonions. Firstly note that any quaternionic polynomial with real coefficients can be factored …