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Equidivisible Kleene monoids and the Elgot-Mezei theorem. (English) Zbl 0685.20048
Let M be a monoid, $$A^*$$ and $$M^*$$ stand for the varying free monoids. A monoid M satisfies the Elgot-Mezei theorem if for any rational relations f: $$A^*\to M$$ and g: $$M\to C^*$$ the composition gf is rational too. The main result in the paper is that equidivisible Kleene monoids satisfy this theorem. The proof and some additional comments are supplied.
Reviewer: K.Peeva

##### MSC:
 20M35 Semigroups in automata theory, linguistics, etc. 20M05 Free semigroups, generators and relations, word problems
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