Bounded lattices with an antitone involution the complemented elements of which do not form a sublattice must contain two complemented elements such that not both their join and their meet are complemented. We distinguish (up to symmetry) eight cases and in each of these cases we present such a lattice of minimal cardinality.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1147,
author = {Ivan Chajda and Helmut L\"anger},
title = {Minimal bounded lattices with an antitone involution the complemented elements of which do not form a sublattice},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {28},
year = {2008},
pages = {251-259},
zbl = {1195.06003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1147}
}
Ivan Chajda; Helmut Länger. Minimal bounded lattices with an antitone involution the complemented elements of which do not form a sublattice. Discussiones Mathematicae - General Algebra and Applications, Tome 28 (2008) pp. 251-259. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1147/
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