2024/11/13 by Artem Lopatin, Lopatin, Artem, Alexandr N. Zubkov +1
Mathematics · #FOS: Mathematics #Mathematics and Applications #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2411.08500
openalex publication_date 2024/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Over an algebraically closed field, we describe the affine varieties of solutions to the linear equations a(xb)=c and a(bx)=c over the split-octonions. We also determine the dimensions of the solution sets of arbitrary linear monomial equations in the split-octonions. Moreover, we show that if a linear monomial equation over the split-octonions with nonzero constant term has at least two solutions, then it necessarily possesses an invertible solution.