Abstract
We call a complete lattice perfect if it is a sublattice of a lattice of the form Sp(A), where A is an algebraic lattice and Sp(A) stands for the lattice of algebraic subsets of A.
The problem of the description of perfect lattices is motivated by the fact that lattices of subquasivarieties are perfect. In our paper, we describe a new class of perfect lattices that we call super lattices. As a corollary, we completely describe perfect lattices of suborders, and show that lattices of subsemilattices that satisfy the weak Jónsson property are perfect. The weak Jónsson property is a slight generalization of the original Jónsson property D(L) = L.
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Presented by R. Freese.
Dedicated to the 60th birthday of Viktor Gorbunov
This research was supported in part by CRDF grant KYM1-2852-BI-07.
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Adaricheva, K. On the prevariety of perfect lattices. Algebra Univers. 65, 21–39 (2011). https://doi.org/10.1007/s00012-011-0115-6
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DOI: https://doi.org/10.1007/s00012-011-0115-6