On the prevariety of perfect lattices

Kira Adaricheva

Research output: Contribution to journalArticle

3 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 2011
Externally publishedYes

Fingerprint

Algebraic Lattice
Superlattices
Complete Lattice
Corollary
Subset
Class
Generalization
Form

Keywords

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

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

On the prevariety of perfect lattices. / Adaricheva, Kira.

In: Algebra Universalis, Vol. 65, No. 1, 02.2011, p. 21-39.

Research output: Contribution to journalArticle

Adaricheva, Kira. / On the prevariety of perfect lattices. In: Algebra Universalis. 2011 ; Vol. 65, No. 1. pp. 21-39.
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