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Associative polynomial functions over bounded distributive lattices

Marichal, Jean-Luc; Couceiro, Miguel (2011), Associative polynomial functions over bounded distributive lattices, Order, 28, 1, p. 1-8. http://dx.doi.org/10.1007/s11083-010-9150-8

Type
Article accepté pour publication ou publié
Lien vers un document non conservé dans cette base
http://arxiv.org/abs/0902.2323
Date
2011
Nom de la revue
Order
Volume
28
Numéro
1
Éditeur
Springer
Pages
1-8
Identifiant publication
Métadonnées
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Auteur(s)
Marichal, Jean-Luc
Couceiro, Miguel
Résumé (EN)
The associativity property, usually defined for binary functions, can be generalized to functions of a given fixed arity n ⩾ 1 as well as to functions of multiple arities. In this paper, we investigate these two generalizations in the case of polynomial functions over bounded distributive lattices and present explicit descriptions of the corresponding associative functions. We also show that, in this case, both generalizations of associativity are essentially the same.
Mots-clés
Bounded distributive lattice; Polynomial function; Associativity; Idempotency; Range-idempotency; Functional equation