On the prevariety of perfect lattices

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 pe...

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Bibliographic Details
Published in:Algebra universalis 2011-02, Vol.65 (1), p.21-39
Main Author: Adaricheva, Kira
Format: Article
Language:English
Subjects:
Algebra
Mathematics
Mathematics and Statistics
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Summary: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 .
ISSN:0002-5240
1420-8911
DOI:10.1007/s00012-011-0115-6