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dc.contributor.authorKioko, Eugene Moses
dc.contributor.authorNjuguna, Lydia
dc.date.accessioned2023-07-10T13:41:53Z
dc.date.available2023-07-10T13:41:53Z
dc.date.issued2020
dc.identifier.issn2454-6194
dc.identifier.urihttp://ir-library.ku.ac.ke/handle/123456789/26146
dc.descriptionarticleen_US
dc.description.abstractHypercomplex 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: 20B05en_US
dc.language.isoenen_US
dc.publisherIJRIASen_US
dc.subjectLoopsen_US
dc.subjectC-loopsen_US
dc.subjectHypercomplex numbersen_US
dc.subjectCayley- Dicksonen_US
dc.subjectSplit extensionen_US
dc.titleC-Loops Obtained From Hypercomplex Numbersen_US
dc.typeArticleen_US


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