𝑄-universal quasivarieties of algebras

Adams, M. E.; Dziobiak, W.

doi:10.1090/S0002-9939-1994-1172942-0

$Q$-universal quasivarieties of algebras
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by M. E. Adams and W. Dziobiak PDF

Proc. Amer. Math. Soc. 120 (1994), 1053-1059 Request permission

Abstract:

A quasivariety of algebras of finite type is $Q$-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 $Q$-universal is given, thereby adding, amongst others, the quasivarieties of de Morgan algebras, Kleene algebras, distributive $p$-algebras, distributive double $p$-algebras, Heyting algebras, double Heyting algebras, lattices containing the modular lattice ${M_{3,3}}, MV$-algebras, and commutative rings with unity to the known $Q$-universal quasivarieties.

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