Over an algebraically closed field, we describe the affine varieties of solutions to the linear equations (ax)b=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.
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Lopatin et al. (2026) studied this question.
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