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- Title
Varieties of Groupoids and Quasigroups Generated by Linear-Bivariate Polynomials Over Ring ℤ<sub>n</sub>.
- Authors
Ilojide, E.; Jaiyéọlá, T. G.; Owojori, O. O.
- Abstract
Some varieties of groupoids and quasigroups generated by linear-bivariate polynomials P(x, y) = a+bx+cy over the ring ℤn are studied. Necessary and sufficient conditions for such groupoids and quasigroups to obey identities which involve one, two, three (e.g. Bol-Moufang type) and four variables w.r.t. a, b and c are established. Necessary and sufficient conditions for such groupoids and quasigroups to obey some inverse properties w.r.t. a, b and c are also established. This class of groupoids and quasigroups are found to belong to some varieties of groupoids and quasigroups such as medial groupoid(quasigroup), F-quasigroup, semi automorphic inverse property groupoid(quasigroup) and automorphic inverse property groupoid(quasigroup).
- Subjects
GROUPOIDS; QUASIGROUPS; POLYNOMIALS; MATHEMATICAL optimization; NUMERICAL analysis; GROUP theory; COMPLEX numbers
- Publication
International Journal of Mathematical Combinatorics, 2011, Vol 2, p79
- ISSN
1937-1055
- Publication type
Article