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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1123,
author = {Aleksandr Kravchenko},
title = {Lattices of relative colour-families and antivarieties},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {27},
year = {2007},
pages = {123-139},
zbl = {1135.08005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1123}
}
Aleksandr Kravchenko. Lattices of relative colour-families and antivarieties. Discussiones Mathematicae - General Algebra and Applications, Tome 27 (2007) pp. 123-139. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1123/
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