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$ Q$-universal quasivarieties of algebras


Authors: M. E. Adams and W. Dziobiak
Journal: Proc. Amer. Math. Soc. 120 (1994), 1053-1059
MSC: Primary 08C15; Secondary 03C05, 03G25, 06Dxx
DOI: https://doi.org/10.1090/S0002-9939-1994-1172942-0
MathSciNet review: 1172942
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1994-1172942-0
Keywords: Quasivariety, lattice of quasivarieties, $ Q$-universality, ideal lattice, Fraser-Horn property
Article copyright: © Copyright 1994 American Mathematical Society

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