All quasitrivial n-ary semigroups are reducible to semigroups

04/11/2019
by   Miguel Couceiro, et al.
0

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.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset