Krohn-Rhodes complexity pseudovarieties are not finitely based
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 39 (2005) no. 1, pp. 279-296.

We prove that the pseudovariety of monoids of Krohn-Rhodes complexity at most n is not finitely based for all n>0. More specifically, for each pair of positive integers n,k, we construct a monoid of complexity n+1, all of whose k-generated submonoids have complexity at most n.

DOI : 10.1051/ita:2005016
Classification : 20M07
Mots clés : complexity, finite basis problem, the presentation lemma
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Rhodes, John; Steinberg, Benjamin. Krohn-Rhodes complexity pseudovarieties are not finitely based. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 39 (2005) no. 1, pp. 279-296. doi : 10.1051/ita:2005016. http://archive.numdam.org/articles/10.1051/ita:2005016/

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