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dc.contributor.authorŁazarz, Marcin
dc.date.accessioned2017-07-10T12:08:38Z
dc.date.available2017-07-10T12:08:38Z
dc.date.issued2016
dc.identifier.issn0138-0680
dc.identifier.urihttp://hdl.handle.net/11089/22185
dc.description.abstractIn the paper we investigate Birkhoff’s conditions (Bi) and (Bi*). We prove that a discrete lattice L satisfies the condition (Bi) (the condition (Bi*)) if and only if L is a 4-cell lattice not containing a cover-preserving sublattice isomorphic to the lattice S*7 (the lattice S7). As a corollary we obtain a well known result of J. Jakubík from [6]. Furthermore, lattices S7 and S*7 are considered as so-called partially cover-preserving sublattices of a given lattice L, S7 ≪ L and S*7 ≪ L, in symbols. It is shown that an upper continuous lattice L satisfies (Bi*) if and only if L is a 4-cell lattice such that S7 ≪ L. The final corollary is a generalization of Jakubík’s theorem for upper continuous and strongly atomic lattices.en_GB
dc.language.isoenen_GB
dc.publisherWydawnictwo Uniwersytetu Łódzkiegoen_GB
dc.relation.ispartofseriesBulletin of the Section of Logic;3/4
dc.subjectBirkhoff’s conditionsen_GB
dc.subjectsemimodularity conditionsen_GB
dc.subjectmodular latticeen_GB
dc.subjectdiscrete latticesen_GB
dc.subjectupper continuous latticeen_GB
dc.subjectstrongly atomic latticeen_GB
dc.subjectcover-preserving sublatticeen_GB
dc.subjectcellen_GB
dc.subject4-cell latticeen_GB
dc.titleCharacterization of Birkhoff’s Conditions by Means of Cover-Preserving and Partially Cover-Preserving Sublatticesen_GB
dc.typeArticleen_GB
dc.rights.holder© Copyright by Authors, Łódź 2016; © Copyright for this edition by Uniwersytet Łódzki, Łódź 2016en_GB
dc.page.number[185]-197
dc.contributor.authorAffiliationUniversity of Wrocław, Department of Logic and Methodology of Sciences
dc.identifier.eissn2449-836X
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dc.contributor.authorEmaillazarzmarcin@poczta.onet.pl
dc.identifier.doi10.18778/0138-0680.45.3.4.04
dc.relation.volume45en_GB


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