Polygroupoid, Polyquasigroup, Polyloop and their Nuclei
Group Theory
2025-04-23 v1
Abstract
In this paper, new hyper-algebraic structures called polygroupoid, polyquasigroup and polyloop were introduced with concrete examples given. The first, second, third and fourth left (middle, right) nuclei of polygroupoid were introduced and studied. It was shown that first left (middle, right) nuclei of a polygroupoid is contained in second, third and fourth left (middle, right) nuclei of the polygroupoid. Hence, the second, third and fourth left (middle, right) nuclei of a polygroupoid generalize the first left (middle, right) nuclei of the polygroupoid. Examples of polyquasigroups and polyloops that satisfy the above results were provided.
Cite
@article{arxiv.2504.15498,
title = {Polygroupoid, Polyquasigroup, Polyloop and their Nuclei},
author = {K. G. Ilori and T. G. Jaiyeola and O. O. Oyebola and O. B. Ogunfolu and E. A. Alhassan},
journal= {arXiv preprint arXiv:2504.15498},
year = {2025}
}
Comments
23 pages