Nonassociativity à la Kleene

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. There-after 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. © Springer-Verlag Berlin Heidelberg 2007.