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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).

Lattice-theoretically characterized classes of finite bands

Reinhard Thron, Jörg Koppitz (2003)

Archivum Mathematicum

There are investigated classes of finite bands such that their subsemigroup lattices satisfy certain lattice-theoretical properties which are related with the cardinalities of the Green’s classes of the considered bands, too. Mainly, there are given disjunctions of equations which define the classes of finite bands.

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