Title : Characterizations of quasitrivial symmetric nondecreasing associative operations
Language : English
Author, co-author : Devillet, Jimmy [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Kiss, Gergely []
Marichal, Jean-Luc [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Publication date : Feb-2019
Journal title : Semigroup Forum
Publisher : Springer
Volume : 98
Issue/season : 1
Pages : 154-171
Peer reviewed : Yes (verified by ORBilu )
Audience : International
ISSN : 0037-1912
e-ISSN : 1432-2137
City : New York
Country : Germany
Keywords : [en] n-ary semigroup ; associativity ; bisymmetry ; ultrabisymmetry ; neutral element ; axiomatization
Abstract : [en] We provide a description of the class of n-ary operations on an arbitrary chain that are quasitrivial, symmetric, nondecreasing, and associative. We also prove that associativity can be replaced with bisymmetry in the definition of this class. Finally we investigate the special situation where the chain is finite.
Funders : University of Luxembourg - UL
Target : Researchers ; Professionals ; Students
Permalink : http://hdl.handle.net/10993/34499
DOI : 10.1007/s00233-018-9980-z
Other URL : https://arxiv.org/abs/1705.00719