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Algebra universalis

, Volume 60, Issue 4, pp 439–468 | Cite as

Cancellation in entropic algebras

  • M. M. StronkowskiEmail author
Article

Abstract.

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. Ježek and T. Kepka in the case of groupoids.

2000 Mathematics Subject Classification:

03C05 08C05 18A40 

Keywords and phrases:

entropic algebra cancellative algebra quasi-affine algebra monoid of terms \({\mathcal{M}}\)-cancellative algebra polyquasigroup \({\mathcal{M}}\)-polyquasigroup equational theory injective reflector 

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Copyright information

© Birkhäuser Verlag, Basel 2009

Authors and Affiliations

  1. 1.Faculty of Mathematics and Information SciencesWarsaw University of TechnologyWarsawPoland

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