A closure condition which is equivalent to the Thomsen condition in quasigroups

Autores: M. A. Taylor
Localización: Stochastica: revista de matemática pura y aplicada, ISSN 0210-7821, Vol. 7, Nº. 1, 1983, págs. 11-16
Idioma: inglés
Títulos paralelos:
- Condición de clausura equivalente a la condición de Thomsen en quasigrupos.
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Resumen
- In this note it is shown that the closure condition, X1Y2 = X2Y1, X1Y4 = X2Y3, X3Y3 = X4Y1 --> X4Y2 = X3Y4, (and its dual) is equivalent to the Thomsen condition in quasigroups but not in general. Conditions are also given under which groupoids satisfying it are principal homotopes of cancellative, abelian semigroups, or abelian groups.