2014
DOI: 10.48550/arxiv.1408.0991
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Varieties of groupoids and quasigroups generated by linear-bivariate polynomials over ring Z_n

Emmanuel Ilojide,
Temitope Gbolahan Jaiyeola,
O. O. Owojori

Abstract: Some varieties of groupoids and quasigroups generated by linear-bivariate polynomials P (x, y) = a + bx + cy over the ring Z n 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 quasig… Show more

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