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Published in:
2006 | OriginalPaper | Chapter
On Finitely Generated Varieties of Distributive Double p-algebras and their Subquasivarieties
Authors : Václav Koubek, Jiří Sichler
Published in: Topics in Discrete Mathematics
Publisher: Springer Berlin Heidelberg
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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.