Resumen de Cancellation in entropic algebras

Michal M. Stronkowski

• 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.