Geodesic
Lattices and semilattices having an antitone involution in every upper interval
Commentationes Mathematicae Universitatis Carolinae, Tome 44 (2003) no. 4, pp. 577-585

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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.
Classification : 06A12, 06C15, 06F35, 08B05, 08B10
Keywords: semilat\/tice; lat\/tice; antitone involution; congruence permutability; weak regularity 
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Chajda, Ivan. Lattices and semilattices having an antitone involution in every upper interval. Commentationes Mathematicae Universitatis Carolinae, Tome 44 (2003) no. 4, pp. 577-585. http://geodesic.mathdoc.fr/item/CMUC_2003__44_4_a1/