Finite atomistic lattices that can be represented as lattices of quasivarieties

K. Adaricheva; Wiesław Dziobiak; V. Gorbunov

Fundamenta Mathematicae (1993)

  • Volume: 142, Issue: 1, page 19-43
  • ISSN: 0016-2736

Abstract

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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].

How to cite

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Adaricheva, K., Dziobiak, Wiesław, and Gorbunov, V.. "Finite atomistic lattices that can be represented as lattices of quasivarieties." Fundamenta Mathematicae 142.1 (1993): 19-43. <http://eudml.org/doc/211969>.

@article{Adaricheva1993,
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].},
author = {Adaricheva, K., Dziobiak, Wiesław, Gorbunov, V.},
journal = {Fundamenta Mathematicae},
keywords = {atomistic lattice; quasivariety; Mal'cev problem; equa-closure operator; semilattice; finite atomistic lattice; lattice of quasivarieties},
language = {eng},
number = {1},
pages = {19-43},
title = {Finite atomistic lattices that can be represented as lattices of quasivarieties},
url = {http://eudml.org/doc/211969},
volume = {142},
year = {1993},
}

TY - JOUR
AU - Adaricheva, K.
AU - Dziobiak, Wiesław
AU - Gorbunov, V.
TI - Finite atomistic lattices that can be represented as lattices of quasivarieties
JO - Fundamenta Mathematicae
PY - 1993
VL - 142
IS - 1
SP - 19
EP - 43
AB - 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].
LA - eng
KW - atomistic lattice; quasivariety; Mal'cev problem; equa-closure operator; semilattice; finite atomistic lattice; lattice of quasivarieties
UR - http://eudml.org/doc/211969
ER -

References

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  3. [3] K. V. Adaricheva, W. Dziobiak and V. A. Gorbunov, The lattices of quasivarieties of locally finite quasivarieties, preprint. Zbl0937.06002
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