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ArticleOriginal scientific text

Title

Finite atomistic lattices that can be represented as lattices of quasivarieties

Authors 1, 2, 1

Affiliations

  1. Institute of Mathematics, Russian Academy of Sciences, Universitetskiĭ Prosp. 4, 630090 Novosibirsk, Russia
  2. Institute of Mathematics, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland

Abstract

We prove that a finite atomistic lattice can be represented as a lattice of quasivarieties if and only if it is isomorphic to the lattice of all subsemilattices of a finite semilattice. This settles a conjecture that appeared in the context of [11].

Keywords

ENG
atomistic lattice, quasivariety, Mal'cev problem, equa-closure operator, semilattice

Bibliography

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Additional information

http://matwbn.icm.edu.pl/ksiazki/fm/fm142/fm14212.pdf

Fundamenta Mathematicae
1993/142/1
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Pages:
19-43
Main language of publication
English
Received
1991-05-20
Accepted
1992-03-03
Published
1993
Exact and natural sciences