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 SM ISO690:2012PHILLIPS, Jon D., PUSHKASHU, D. I., SHCHERBACOV, Alexei, SHCHERBACOV, Victor. On Birkhoff's quasigroup axioms. In: Journal of Algebra, 2016, nr. 457, pp. 7-17. ISSN 0021-8693. DOI: https://doi.org/10.1016/j.jalgebra.2016.02.024 |
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 Journal of Algebra |
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| Numărul 457 / 2016 / ISSN 0021-8693 /ISSNe 1090-266X | ||||||
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| DOI:https://doi.org/10.1016/j.jalgebra.2016.02.024 | ||||||
| Pag. 7-17 | ||||||
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Birkhoff defined a quasigroup as an algebra (Q, ⋅, \, /) that satisfies the following six identities: x⋅. (x\y) = y, (y/x) ⋅ x = y, x\(x ⋅ y) = y, (y ⋅ x)/x = y, x/(y\x) = y, and (x/y) \ x = y. We investigate triples and tetrads of identities composed of these six, emphasizing those that axiomatize the variety of quasigroups. |
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| Cuvinte-cheie (Equational) quasigroup, (Left) quasigroup, cancellation groupoid, Division groupoid |
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