Associative polynomial functions over bounded distributive lattices

Details Associative polynomial functions over bounded distributive lattices Associative polynomial functions over bounded distributive lattices

2009-02-13

arxiv.org/abs/0902.2323v4

Order - A Journal on the Theory of Ordered Sets and its Applications 28 (1) (2011) 1-8

Mathematics

Rings and Algebras

Final version

Scientific paper

10.1007/s11083-010-9150-8

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.

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