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Journal Articles Algebra Universalis Year : 2019

Every quasitrivial n-ary semigroup is reducible to a semigroup

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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.
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Dates and versions

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

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Miguel Couceiro, Jimmy Devillet. Every quasitrivial n-ary semigroup is reducible to a semigroup. Algebra Universalis, 2019, 8 (4), 19 p. ⟨10.1007/s00012-019-0626-0⟩. ⟨hal-02099236v2⟩
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