4 citations · 4 across the 5 of their papers we have counts for
5 papers
Points with Commuting Coordinates over Division Rings
Adam Chapman, Solomon Vishkautsan
We investigate the properties of multivariate polynomials evaluated at points with commuting coordinates over division rings and octonion algebras. Given a division ring , this…
General Polynomials and Eigenvalues Over Cayley--Dickson Algebras
Adam Chapman, Ilan Levin, Solomon Vishkautsan
In this paper, we provide an explicit method for determining the zero set of monic quadratic general polynomials over Cayley--Dickson algebras with any base field of characteristic…
Central Products of Cayley-Dickson Loops
Adam Chapman, Ilan Levin
This paper studies the triviality of commutators in central products of Cayley-Dickson loops. Two immediate outcomes of this study are (1) the construction of a sequence of non-com…
Recurrence relations over division algebras
Adam Chapman, Solomon Vishkautsan
We generalize the solution of linear recurrence relations from fields to central division algebras, adapting the standard tools of companion matrices and characteristic polynomials…
Roots and right factors of polynomials and left eigenvalues of matrices over Cayley-Dickson algebras
Adam Chapman, Solomon Vishkautsan
Over a composition algebra , a polynomial has a root if and only for some . We examine whether this is true for general…