All quasitrivial n-ary semigroups are reducible to semigroups - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Preprints, Working Papers, ... Year : 2019

All quasitrivial n-ary semigroups are reducible to semigroups

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.
Fichier principal
Vignette du fichier
CharacterizationsQuasi-tivial10042019.pdf (387.9 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-02099236 , version 1 (14-04-2019)
hal-02099236 , version 2 (29-08-2019)

Identifiers

  • HAL Id : hal-02099236 , version 1

Cite

Miguel Couceiro, Jimmy Devillet. All quasitrivial n-ary semigroups are reducible to semigroups. 2019. ⟨hal-02099236v1⟩
88 View
167 Download

Share

Gmail Facebook X LinkedIn More