Nonassociativity à la Kleene

Authors:
Jean-Marcel Pallo
Affiliations:
Universit de Bourgogne, LE2I, UMR, Dijon-Cedex, France
Venue:
CAI'07 Proceedings of the 2nd international conference on Algebraic informatics
Year:
2007

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Abstract

First we recall the work of Suschkewitsch (1929) about the generalization of the associative law which is the starting point of the theory of quasigroups. Then we show that it is a particular case of the notion of relative associativity introduced by Roubaud in 1965. Thereafter we prove a coherence theorem over an infinite set of nonassociative operations. This result contains all the uppermentioned contributions. This allows to obtain a very general à-la-Kleene theorem on rational series which uses concatenations that can be associative or not.