Reference : Decomposition schemes for symmetric n-ary bands
Scientific congresses, symposiums and conference proceedings : Unpublished conference
Physical, chemical, mathematical & earth Sciences : Mathematics
Engineering, computing & technology : Computer science
Computational Sciences
http://hdl.handle.net/10993/44126
Decomposition schemes for symmetric n-ary bands
English
Devillet, Jimmy mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Mathonet, Pierre []
27-Aug-2020
Yes
International
1st International Conference on Algebras, Graphs and Ordered Sets (ALGOS 2020)
from 26-08-2020 to 28-08-2020
LORIA (Université de Lorraine, CNRS, Inria Nancy G.E.)
Nancy
France
[en] Semigroup ; idempotency ; semilattice decomposition ; reducibility
[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.
Fonds National de la Recherche - FnR
Researchers ; Professionals ; Students
http://hdl.handle.net/10993/44126
https://hal.archives-ouvertes.fr/hal-02918958
https://algos2020.loria.fr/
FnR ; FNR10949314 > Gabor Wiese > GSM > Geometric and Stochastic Methods in Mathematics and Applications > 01/10/2016 > 31/03/2023 > 2016

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