Some results on $𝒞$-varieties
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 39 (2005) no. 1, pp. 239-262.

In an earlier paper, the second author generalized Eilenberg’s variety theory by establishing a basic correspondence between certain classes of monoid morphisms and families of regular languages. We extend this theory in several directions. First, we prove a version of Reiterman’s theorem concerning the definition of varieties by identities, and illustrate this result by describing the identities associated with languages of the form ${\left({a}_{1}{a}_{2}\cdots {a}_{k}\right)}^{+}$, where ${a}_{1},...,{a}_{k}$ are distinct letters. Next, we generalize the notions of Mal’cev product, positive varieties, and polynomial closure. Our results not only extend those already known, but permit a unified approach of different cases that previously required separate treatment.

DOI : https://doi.org/10.1051/ita:2005014
Classification : 20M35,  68Q70
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Pin, Jean-Éric; Straubing, Howard. Some results on $\mathcal {C}$-varieties. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 39 (2005) no. 1, pp. 239-262. doi : 10.1051/ita:2005014. http://www.numdam.org/articles/10.1051/ita:2005014/

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