[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 :
Computer science Mathematics
Author, co-author :
Devillet, Jimmy ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Mathonet, Pierre
External co-authors :
yes
Language :
English
Title :
Decomposition schemes for symmetric n-ary bands
Publication date :
27 August 2020
Event name :
1st International Conference on Algebras, Graphs and Ordered Sets (ALGOS 2020)
Event organizer :
LORIA (Université de Lorraine, CNRS, Inria Nancy G.E.)
