On the modular relation in atomistic lattices
M. Janowitz (1970)
Fundamenta Mathematicae
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M. Janowitz (1970)
Fundamenta Mathematicae
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Walendziak, Andrzej (1994)
Portugaliae Mathematica
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M. Janowitz (1975)
Fundamenta Mathematicae
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Marcin Łazarz (2016)
Bulletin of the Section of Logic
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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. Jakub´ık 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 S7...
Henry H. Crapo (1967)
Rendiconti del Seminario Matematico della Università di Padova
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David Sachs (1966)
Rendiconti del Seminario Matematico della Università di Padova
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Andrzej Walendziak (2004)
Czechoslovak Mathematical Journal
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The aim of this paper is to present relations between Goldie, hollow and Kurosh-Ore dimensions of semimodular lattices. Relations between Goldie and Kurosh-Ore dimensions of modular lattices were studied by Grzeszczuk, Okiński and Puczyłowski.