Geodesic
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

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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
Keywords: complexity, finite basis problem, the presentation lemma 
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     author = {Rhodes, John and Steinberg, Benjamin},
     title = {Krohn-Rhodes complexity pseudovarieties are not finitely based},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {279--296},
     publisher = {EDP-Sciences},
     volume = {39},
     number = {1},
     year = {2005},
     doi = {10.1051/ita:2005016},
     mrnumber = {2132592},
     zbl = {1083.20050},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ita:2005016/}
}
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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

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