[en] We extend the classical (strong) semilattice decomposition scheme of certain classes of semigroups to the class of idempotent symmetric n-ary semigroups (i.e. symmetric n-ary bands) where n \geq 2 is an integer. More precisely, we show that these semigroups are exactly the strong n-ary semilattices of n-ary extensions of Abelian groups whose exponents divide n-1. We then use this main result to obtain necessary and sufficient conditions for a symmetric n-ary band to be reducible to a semigroup.
Disciplines :
Sciences informatiques Mathématiques
Auteur, co-auteur :
DEVILLET, Jimmy ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Mathonet, Pierre
Co-auteurs externes :
yes
Langue du document :
Anglais
Titre :
Decomposition schemes for symmetric n-ary bands
Date de publication/diffusion :
27 août 2020
Nom de la manifestation :
1st International Conference on Algebras, Graphs and Ordered Sets (ALGOS 2020)
Organisateur de la manifestation :
LORIA (Université de Lorraine, CNRS, Inria Nancy G.E.)
