Reference : On the structure of symmetric $n$-ary bands
 Document type : E-prints/Working papers : First made available on ORBilu Discipline(s) : Physical, chemical, mathematical & earth Sciences : Mathematics To cite this reference: http://hdl.handle.net/10993/43023
 Title : On the structure of symmetric $n$-ary bands Language : English Author, co-author : Devillet, Jimmy [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >] Mathonet, Pierre [] Publication date : 2020 Peer reviewed : No Keywords : [en] Semigroup ; polyadic semigroup ; semilattice decomposition ; reducibility ; idempotency Abstract : [en] We study the class of symmetric $n$-ary bands. These are $n$-ary semigroups $(X,F)$ such that $F$ is invariant under the action of permutations and idempotent, i.e., satisfies $F(x,\ldots,x)=x$ for all $x\in X$. We first provide a structure theorem for these symmetric $n$-ary bands that extends the classical (strong) semilattice decomposition of certain classes of bands. We introduce the concept of strong $n$-ary semilattice of $n$-ary semigroups and we show that the symmetric $n$-ary bands are exactly the strong $n$-ary semilattices of $n$-ary extensions of Abelian groups whose exponents divide $n-1$. Finally, we use the structure theorem to obtain necessary and sufficient conditions for a symmetric $n$-ary band to be reducible to a semigroup. Funders : Fonds National de la Recherche - FnR Target : Researchers ; Professionals ; Students Permalink : http://hdl.handle.net/10993/43023 FnR project : FnR ; FNR10949314 > Gabor Wiese > GSM > Geometric and Stochastic Methods in Mathematics and Applications > 01/10/2016 > 31/03/2023 > 2016

File(s) associated to this reference

Fulltext file(s):

FileCommentaryVersionSizeAccess
Open access
Symmetricnaryband.pdfAuthor preprint331.85 kBView/Open

All documents in ORBilu are protected by a user license.