On Birkhoff&#39;s quasigroup axioms

Phillips Jon D.; Pushkashu D. I.; Shcherbacov Alexei; Shcherbacov Victor

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2024-05-27 11:19

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PHILLIPS, 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

Numărul 457 / 2016 / ISSN 0021-8693 /ISSNe 1090-266X

On Birkhoff's quasigroup axioms

DOI:https://doi.org/10.1016/j.jalgebra.2016.02.024

Pag. 7-17

Phillips Jon D.¹, Pushkashu D. I.², Shcherbacov Alexei³, Shcherbacov Victor²

¹ University of Michigan,
² Institute of Mathematics and Computer Science ASM,
³ Liceul Teoretic „C.Sibirschii” din Chişinău

Disponibil în IBN: 1 ianuarie 2023

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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.

Cuvinte-cheie
(Equational) quasigroup, (Left) quasigroup, cancellation groupoid, Division groupoid

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