Abstract
A quasivariety ℚ is Q-universal if, for any quasivariety \( \mathbb{V} \) of algebraic systems of a finite similarity type, the lattice L(\( \mathbb{V} \)) of all subquasivarieties of \( \mathbb{V} \) is isomorphic to a quotient lattice of a sublattice of the lattice L(ℚ) of all subquasivarieties of ℚ. We investigate Q-universality of finitely generated varieties of distributive double p-algebras. In an earlier paper, we proved that any finitely generated variety of distributive double p-algebras categorically universal modulo a group is also Q-universa1. Here we consider the remaining finitely generated varieties of distributive double p-algebras and state a problem whose solution would complete the description of all Q-universal finitely generated varieties of distributive double p-algebras.
The authors gratefully acknowledge the support of 1M0021620808, a project of the Czech Ministry of Education and of the NSERC of Canada.
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Koubek, V., Sichler, J. (2006). On Finitely Generated Varieties of Distributive Double p-algebras and their Subquasivarieties. In: Klazar, M., Kratochvíl, J., Loebl, M., Matoušek, J., Valtr, P., Thomas, R. (eds) Topics in Discrete Mathematics. Algorithms and Combinatorics, vol 26. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-33700-8_5
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