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 $n$ .

Krohn-Rhodes complexity pseudovarieties are not finitely based

John Rhodes; Benjamin Steinberg — 2010

RAIRO - Theoretical Informatics and Applications

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

Hecke operators for GLₙ and buildings

Cristina M. Ballantine; John A. Rhodes; Thomas R. Shemanske — 2004

Acta Arithmetica

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