31 citations · 57 across the 8 of their papers we have counts for
12 papers
On the structure of symmetric -ary bands
Jimmy Devillet, Pierre Mathonet
We study the class of symmetric -ary bands. These are -ary semigroups such that is invariant under the action of permutations and idempotent, i.e., satisfies $F(x…
Reducibility of -ary semigroups: from quasitriviality towards idempotency
Miguel Couceiro, Jimmy Devillet, Jean-Luc Marichal +1
Let be a nonempty set. Denote by the class of associative operations satisfying the condition when…
Every quasitrivial n-ary semigroup is reducible to a semigroup
Miguel Couceiro, Jimmy Devillet
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 resu…
Classifications of quasitrivial semigroups
Jimmy Devillet, Jean-Luc Marichal, Bruno Teheux
We investigate classifications of quasitrivial semigroups defined by certain equivalence relations. The subclass of quasitrivial semigroups that preserve a given total ordering is…
Invariance in a class of operations related to weighted quasi-geometric means
Jimmy Devillet, Janusz Matkowski
Let be an interval that is closed with respect to the multiplication. The operations of the form \begin{equation*} C_{f,g}…
A new invariance identity and means
Jimmy Devillet, Janusz Matkowski
The invariance identity involving three operations of the form \begin{equation*} D_{f,g}\left( x,y\right) =\left( f\circ g\right) ^{-1}\left( f\lef…