On the prevariety of perfect lattices

Kira Adaricheva

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)21-39
Number of pages19
JournalAlgebra Universalis
Volume65
Issue number1
DOIs
Publication statusPublished - Feb 1 2011

Keywords

  • Jónsson property
  • congruence lattice of a semilattice
  • join-semidistributive lattice
  • lattice of suborders
  • lattice of subsemilattices
  • lower bounded lattice

ASJC Scopus subject areas

  • Algebra and Number Theory

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