3 citations · 3 across the 5 of their papers we have counts for
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On polynomial equations over split-octonions: the arbitrary field case
Artem Lopatin
Over the split-octonion algebra defined over an arbitrary field, we solve all polynomial equations whose coefficients are scalar except for the constant term. As an application, we…
On polynomial equations over split octonions
Artem Lopatin, Alexander N. Rybalov
Working over the split octonions over an algebraically closed field, we solve all polynomial equations in which all the coefficients but the constant term are scalar. As a conseque…
Classification of four-dimensional anti-dendriform algebras whose associated associative algebra has the center of dimension one
Jobir Adashev, Artem Lopatin, Zafar Normatov +1
This article is devoted to the classification of anti-dendriform algebras that are associated with associativity. They are characterized as algebras with two operations whose sum i…
On linear equations over split-octonions
Artem Lopatin, Alexandr N. Zubkov
Over an algebraically closed field, we describe the affine varieties of solutions to the linear equations and over the split-octonions. We also determine the di…
Pairs of matrices with simple spectrum
Jennyfer Juliana Calderón Moreno, Artem Lopatin
We established two-sided Curto-Herrero conjecture for pairs of matrices, where the first matrix has a simple spectrum. Namely, it is shown that these pairs are separated by ranks o…