Krohn-Rhodes complexity pseudovarieties are not finitely based
Rhodes, John ; Steinberg, Benjamin
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 39 (2005), p. 279-296 / Harvested from Numdam

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.

Publié le : 2005-01-01
DOI : https://doi.org/10.1051/ita:2005016
Classification:  20M07
@article{ITA_2005__39_1_279_0,
     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},
     volume = {39},
     year = {2005},
     pages = {279-296},
     doi = {10.1051/ita:2005016},
     mrnumber = {2132592},
     zbl = {1083.20050},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ITA_2005__39_1_279_0}
}
Rhodes, John; Steinberg, Benjamin. Krohn-Rhodes complexity pseudovarieties are not finitely based. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 39 (2005) pp. 279-296. doi : 10.1051/ita:2005016. http://gdmltest.u-ga.fr/item/ITA_2005__39_1_279_0/

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