Cancellation in entropic algebras

• Autores: Michal M. Stronkowski
• Localización: Algebra universalis, ISSN 0002-5240, Vol. 60, Nº. 4, 2009, págs. 439-468
• Idioma: inglés
• DOI: 10.1007/s00012-009-2132-2
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• Resumen

  • We describe the equational theory of the class of cancellative entropic algebras of a fixed type. We prove that a cancellative entropic algebra embeds into an entropic polyquasigroup, a natural generalization of a quasigroup. In fact our results are even more general and some corollaries hold also for non-entropic algebras. For instance an algebra with a binary cancellative term operation, which is a homomorphism, is quasi-affine. This gives a strengthening of K. Kearnes� theorem. Our results generalize theorems obtained earlier by M. Sholander and by J. Je�ek and T. Kepka in the case of groupoids.