Geodesic
A classification of rational languages by semilattice-ordered monoids
Archivum mathematicum, Tome 40 (2004) no. 4, pp. 395-406.

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We prove here an Eilenberg type theorem: the so-called conjunctive varieties of rational languages correspond to the pseudovarieties of finite semilattice-ordered monoids. Taking complements of members of a conjunctive variety of languages we get a so-called disjunctive variety. We present here a non-trivial example of such a variety together with an equational characterization of the corresponding pseudovariety.
Classification : 06F05, 08A70, 16Y60, 20M07, 68Q70
Keywords: syntactic semilattice-ordered monoid; conjunctive varieties of rational languages 
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     author = {Pol\'ak, Libor},
     title = {A classification of rational languages by semilattice-ordered monoids},
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Polák, Libor. A classification of rational languages by semilattice-ordered monoids. Archivum mathematicum, Tome 40 (2004) no. 4, pp. 395-406. http://geodesic.mathdoc.fr/item/ARM_2004__40_4_a7/