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On the solidity of general varieties of tree languages

Magnus Steinby (2012)

Discussiones Mathematicae - General Algebra and Applications

For a class of hypersubstitutions 𝓚, we define the 𝓚-solidity of general varieties of tree languages (GVTLs) that contain tree languages over all alphabets, general varieties of finite algebras (GVFAs), and general varieties of finite congruences (GVFCs). We show that if 𝓚 is a so-called category of substitutions, a GVTL is 𝓚-solid exactly in case the corresponding GVFA, or the corresponding GVFC, is 𝓚-solid. We establish the solidity status of several known GVTLs with respect to certain categories...

On universality of semigroup varieties

Marie Demlová, Václav Koubek (2006)

Archivum Mathematicum

A category K is called α -determined if every set of non-isomorphic K -objects such that their endomorphism monoids are isomorphic has a cardinality less than α . A quasivariety Q is called Q -universal if the lattice of all subquasivarieties of any quasivariety of finite type is a homomorphic image of a sublattice of the lattice of all subquasivarieties of Q . We say that a variety V is var-relatively alg-universal if there exists a proper subvariety W of V such that homomorphisms of V whose image does...

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