Lattices of relative colour-families and antivarieties

Aleksandr Kravchenko

Discussiones Mathematicae - General Algebra and Applications (2007)

  • Volume: 27, Issue: 1, page 123-139
  • ISSN: 1509-9415

Abstract

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We consider general properties of lattices of relative colour-families and antivarieties. Several results generalise the corresponding assertions about colour-families of undirected loopless graphs, see [1]. Conditions are indicated under which relative colour-families form a lattice. We prove that such a lattice is distributive. In the class of lattices of antivarieties of relation structures of finite signature, we distinguish the most complicated (universal) objects. Meet decompositions in lattices of colour-families are considered. A criterion is found for existence of irredundant meet decompositions. A connection is found between meet decompositions and bases for anti-identities.

How to cite

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Aleksandr Kravchenko. "Lattices of relative colour-families and antivarieties." Discussiones Mathematicae - General Algebra and Applications 27.1 (2007): 123-139. <http://eudml.org/doc/276835>.

@article{AleksandrKravchenko2007,
abstract = {We consider general properties of lattices of relative colour-families and antivarieties. Several results generalise the corresponding assertions about colour-families of undirected loopless graphs, see [1]. Conditions are indicated under which relative colour-families form a lattice. We prove that such a lattice is distributive. In the class of lattices of antivarieties of relation structures of finite signature, we distinguish the most complicated (universal) objects. Meet decompositions in lattices of colour-families are considered. A criterion is found for existence of irredundant meet decompositions. A connection is found between meet decompositions and bases for anti-identities.},
author = {Aleksandr Kravchenko},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {colour-family; antivariety; lattice of antivarieties; meet decomposition; basis for anti-identities},
language = {eng},
number = {1},
pages = {123-139},
title = {Lattices of relative colour-families and antivarieties},
url = {http://eudml.org/doc/276835},
volume = {27},
year = {2007},
}

TY - JOUR
AU - Aleksandr Kravchenko
TI - Lattices of relative colour-families and antivarieties
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2007
VL - 27
IS - 1
SP - 123
EP - 139
AB - We consider general properties of lattices of relative colour-families and antivarieties. Several results generalise the corresponding assertions about colour-families of undirected loopless graphs, see [1]. Conditions are indicated under which relative colour-families form a lattice. We prove that such a lattice is distributive. In the class of lattices of antivarieties of relation structures of finite signature, we distinguish the most complicated (universal) objects. Meet decompositions in lattices of colour-families are considered. A criterion is found for existence of irredundant meet decompositions. A connection is found between meet decompositions and bases for anti-identities.
LA - eng
KW - colour-family; antivariety; lattice of antivarieties; meet decomposition; basis for anti-identities
UR - http://eudml.org/doc/276835
ER -

References

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