dc.contributor.author | Łazarz, Marcin | |
dc.date.accessioned | 2017-07-10T12:08:38Z | |
dc.date.available | 2017-07-10T12:08:38Z | |
dc.date.issued | 2016 | |
dc.identifier.issn | 0138-0680 | |
dc.identifier.uri | http://hdl.handle.net/11089/22185 | |
dc.description.abstract | In 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.iso | en | en_GB |
dc.publisher | Wydawnictwo Uniwersytetu Łódzkiego | en_GB |
dc.relation.ispartofseries | Bulletin of the Section of Logic;3/4 | |
dc.subject | Birkhoff’s conditions | en_GB |
dc.subject | semimodularity conditions | en_GB |
dc.subject | modular lattice | en_GB |
dc.subject | discrete lattices | en_GB |
dc.subject | upper continuous lattice | en_GB |
dc.subject | strongly atomic lattice | en_GB |
dc.subject | cover-preserving sublattice | en_GB |
dc.subject | cell | en_GB |
dc.subject | 4-cell lattice | en_GB |
dc.title | Characterization of Birkhoff’s Conditions by Means of Cover-Preserving and Partially Cover-Preserving Sublattices | en_GB |
dc.type | Article | en_GB |
dc.rights.holder | © Copyright by Authors, Łódź 2016; © Copyright for this edition by Uniwersytet Łódzki, Łódź 2016 | en_GB |
dc.page.number | [185]-197 | |
dc.contributor.authorAffiliation | University of Wrocław, Department of Logic and Methodology of Sciences | |
dc.identifier.eissn | 2449-836X | |
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dc.contributor.authorEmail | lazarzmarcin@poczta.onet.pl | |
dc.identifier.doi | 10.18778/0138-0680.45.3.4.04 | |
dc.relation.volume | 45 | en_GB |