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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… Click to show full 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.
Keywords:
semigroup reducible;
semigroup;
reducible semigroup;
quasitrivial ary;
ary semigroup;
every quasitrivial
Journal Title: Algebra universalis
Year Published: 2019
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Journal Title: Algebra universalis
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!