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Title: Lattices and semilattices having an antitone involution in every upper interval (English)
Author: Chajda, Ivan
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 44
Issue: 4
Year: 2003
Pages: 577-585
Category: math
Summary: 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. (English)
Keyword: semilat\/tice
Keyword: lat\/tice
Keyword: antitone involution
Keyword: congruence permutability
Keyword: weak regularity
MSC: 06A12
MSC: 06C15
MSC: 06F35
MSC: 08B05
MSC: 08B10
idZBL: Zbl 1101.06003
idMR: MR2062874
Date available: 2009-01-08T19:31:19Z
Last updated: 2012-04-30
Stable URL:
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Reference: [3] Chajda I.: An extension of relative pseudocomplementation to non-distributive lattices.Acta Sci. Math. (Szeged), to appear. Zbl 1048.06005, MR 2034188
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