On the prevariety of perfect lattices (Q535109)
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scientific article; zbMATH DE number 5886748
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the prevariety of perfect lattices |
scientific article; zbMATH DE number 5886748 |
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On the prevariety of perfect lattices (English)
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11 May 2011
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The author deals with the prevariety of perfect lattices. She calls a complete lattice perfect if it is a sublattice of a lattice of the form \(\text{Sp}(A)\), where \(A\) is an algebraic lattice and \(\text{Sp}(A)\) is the lattice of algebraic subsets of \(A\). In this paper she describes a new class of perfect lattices that she calls superlattices. As a corollary she completely describes perfect lattices of suborders, and shows 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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join-semidistributive lattice
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lower-bounded lattice
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Jónsson property
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lattice of suborders
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lattice of subsemilattices
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congruence lattice of a semilattice
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complete lattice
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