Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.08500 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911284070449152 |
|---|---|
| author | Lopatin, Artem Zubkov, Alexandr N. |
| author_facet | Lopatin, Artem Zubkov, Alexandr N. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_08500 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On linear equations over split-octonions Lopatin, Artem Zubkov, Alexandr N. Rings and Algebras 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. |
| title | On linear equations over split-octonions |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2411.08500 |