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Krohn-Rhodes complexity pseudovarieties are not finitely based

John Rhodes, Benjamin Steinberg (2005)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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 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.

Kurepa's functional equation on semigroups.

Bruce R. Ebanks (1982)

Stochastica

The functional equation to which the title refers is:F(x,y) + F(xy,z) = F(x,yz) + F(y,z),where x, y and z are in a commutative semigroup S and F: S x S --> X with (X,+) a divisible abelian group (Divisibility means that for any y belonging to X and natural number n there exists a (unique) solution x belonging to X to nx = y).

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