We study $\vee$-semilat\/tices and lat\/tices with the greatest element 1 where every interval [p,1] is a lat\/tice with an antitone involution. We characterize these semilat\/tices by means of an induced binary operation, the so called sectionally antitone involution. This characterization is done by means of identities, thus the classes of these semilat\/tices or lat\/tices form varieties. The congruence properties of these varieties are investigated.
@article{119412,
author = {Ivan Chajda},
title = {Lattices and semilattices having an antitone involution in every upper interval},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {44},
year = {2003},
pages = {577-585},
zbl = {1101.06003},
mrnumber = {2062874},
language = {en},
url = {http://dml.mathdoc.fr/item/119412}
}
Chajda, Ivan. Lattices and semilattices having an antitone involution in every upper interval. Commentationes Mathematicae Universitatis Carolinae, Tome 44 (2003) pp. 577-585. http://gdmltest.u-ga.fr/item/119412/
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