-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 -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 -universal is given, thereby adding, amongst others, the quasivarieties of de Morgan algebras, Kleene algebras, distributive -algebras, distributive double -algebras, Heyting algebras, double Heyting algebras, lattices containing the modular lattice -algebras, and commutative rings with unity to the known -universal quasivarieties.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1994-1172942-0

Keywords:
Quasivariety,
lattice of quasivarieties,
-universality,
ideal lattice,
Fraser-Horn property

Article copyright:
© Copyright 1994
American Mathematical Society