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Algebra universalis

, 80:51 | Cite as

Every quasitrivial n-ary semigroup is reducible to a semigroup

  • Miguel CouceiroEmail author
  • Jimmy Devillet
Article
  • 21 Downloads

Abstract

We show that every quasitrivial n-ary semigroup is reducible to a binary semigroup, and we provide necessary and sufficient conditions for such a reduction to be unique. These results are then refined in the case of symmetric n-ary semigroups. We also explicitly determine the sizes of these classes when the semigroups are defined on finite sets. As a byproduct of these enumerations, we obtain several new integer sequences.

Mathematics Subject Classification

05A15 20N15 16B99 20M14 

Keywords

Quasitrivial polyadic semigroup Reducibility Enumeration Symmetry 

Notes

Acknowledgements

Both authors would like to thank Jean-Luc Marichal and the anonymous referee for their useful comments and insightful remarks that helped improving the current paper.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Université de Lorraine, CNRS, Inria, LORIANancyFrance
  2. 2.Mathematics Research UnitUniversity of LuxembourgEsch-sur-AlzetteLuxembourg

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