Abstract
A quasivariety of algebras of finite type is Q Q -universal if its lattice of subquasivarieties has, as a homomorphic image of a sublattice, the lattice of subquasivarieties of any quasivariety of algebras of finite type. A sufficient condition for a quasivariety to be Q Q -universal is given, thereby adding, amongst others, the quasivarieties of de Morgan algebras, Kleene algebras, distributive p p -algebras, distributive double p p -algebras, Heyting algebras, double Heyting algebras, lattices containing the modular lattice M 3 , 3 , M V {M_{3,3}},\,MV -algebras, and commutative rings with unity to the known Q Q -universal quasivarieties.
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