# Lattices of relative colour-families and antivarieties

Discussiones Mathematicae - General Algebra and Applications (2007)

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

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topAleksandr 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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