Every quasitrivial n-ary semigroup is reducible to a semigroup

Reference : Every quasitrivial n-ary semigroup is reducible to a semigroup


	Document type :	Scientific journals : Article
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics
	To cite this reference:	http://hdl.handle.net/10993/39337

Title :	Every quasitrivial n-ary semigroup is reducible to a semigroup
Language :	English
Author, co-author :	Couceiro, Miguel []
	Devillet, Jimmy [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Publication date :	Dec-2019
Journal title :	Algebra Universalis
Publisher :	Birkhauser Verlag
Volume :	80
Issue/season :	4
Peer reviewed :	Yes (verified by ORBi^lu)
Audience :	International
ISSN :	0002-5240
e-ISSN :	1420-8911
Country :	Switzerland
Keywords :	[en] quasitrivial polyadic semigroup ; reducibility ; unique reduction ; symmetry ; enumeration
Abstract :	[en] 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 results are then refined in the case of symmetric n-ary semigroups. We also explicitly determine the sizes of these classes when the semigroups are defined on finite sets. As a byproduct of these enumerations, we obtain several new integer sequences.
Funders :	Fonds National de la Recherche - FnR
Target :	Researchers
Permalink :	http://hdl.handle.net/10993/39337
DOI :	10.1007/s00012-019-0626-0

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Open access	NSemigroups-MC-JD-REV.pdf		Author preprint	430.56 kB	View/Open
Limited access	Couceiro-Devillet2019_Article_EveryQuasitrivialN-arySemigrou.pdf		Publisher postprint	457.61 kB	Request a copy

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