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math.RA2024★ 3 cited
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…
math.RA2024
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…
math.RA2024
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…