C-Loops Obtained From Hypercomplex Numbers
| dc.contributor.author | Kioko, Eugene Moses | |
| dc.contributor.author | Njuguna, Lydia | |
| dc.date.accessioned | 2023-07-10T13:41:53Z | |
| dc.date.available | 2023-07-10T13:41:53Z | |
| dc.date.issued | 2020 | |
| dc.description | article | en_US |
| dc.description.abstract | Hypercomplex numbers have played a notable and critical role in the study and exploration of Loop Theory. Researchers have made numerous studies in this area especially in the investigation and construction of different loops. This paper has extended the research to C-loops where we are investigating the formation of C-loops obtained from hypercomplex numbers of dimension 2n ; 1 ≥ n ≤ 4. We are specifically working with the 24- dimensional algebra, called the sedenions. In constructing the C-loops, we have used the frame multiplication of hypercomplex numbers using the Cayley- Dickson construction. We have tested the satisfaction of the left, (x x) (y z) = (x (x y)) z and right, x ((y z) z) = (x y) (z z) C-loop identities by the sedenions. We have also formed split extension of sedenions and equally tested the satisfaction of the C-loop identities on them. We have found that the sedenions satisfy the C-loop identities hence forming C-loops. However, the split extension of sedenions satisfies the right C-loop identity only. AMS Subject Classification: 20B05 | en_US |
| dc.identifier.issn | 2454-6194 | |
| dc.identifier.uri | http://ir-library.ku.ac.ke/handle/123456789/26146 | |
| dc.language.iso | en | en_US |
| dc.publisher | IJRIAS | en_US |
| dc.subject | Loops | en_US |
| dc.subject | C-loops | en_US |
| dc.subject | Hypercomplex numbers | en_US |
| dc.subject | Cayley- Dickson | en_US |
| dc.subject | Split extension | en_US |
| dc.title | C-Loops Obtained From Hypercomplex Numbers | en_US |
| dc.type | Article | en_US |
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