101 citations · 126 across the 18 of their papers we have counts for
8 papers · 1 filter
Roots and Critical Points of Polynomials over Cayley--Dickson Algebras
Adam Chapman, Alexander Guterman, Solomon Vishkautsan +1
We study the roots of polynomials over Cayley--Dickson algebras over an arbitrary field and of arbitrary dimension. For this purpose we generalize the concept of spherical roots fr…
Algebras of slowly growing length
Alexander Guterman, Dmitry Kudryavtsev
We investigate the class of finite dimensional not necessary associative algebras that have slowly growing length, that is, for any algebra in this class its length is less than or…
Steady growth of length function and Malcev algebras
Alexander Guterman, Dmitry Kudryavtsev
We introduce and investigate the algebras of steadily growing length, that is the class of algebras, where the length is bounded by a linear function of the dimension. In particula…
Values of the length function for nonassociative algebras
Alexander Guterman, Dmitry Kudryavtsev
We study realizable values of the length function for unital possibly nonassociative algebras of a given dimension. To do this we apply the method of characteristic sequences and e…
Orthogonality for tropical normal matrices
Bakhad Bakhadly, Alexander Guterman, María Jesús de la Puente
We study pairs of mutually orthogonal normal matrices with respect to tropical multiplication. Minimal orthogonal pairs are characterized. The diameter and girth of three graphs ar…
Linear functions preserving Green's relations over fields
Alexander Guterman, Marianne Johnson, Mark Kambites +1
We study linear functions on the space of matrices over a field which preserve or strongly preserve each of Green's equivalence relations (, …