On Raney's theorems for completely distributive complete lattices
Gabriele H. Greco (1988)
Colloquium Mathematicae
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Gabriele H. Greco (1988)
Colloquium Mathematicae
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Henri Mühle (2023)
Mathematica Bohemica
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This paper is an erratum of H. Mühle: Distributive lattices have the intersection property, Math. Bohem. (2021). Meet-distributive lattices form an intriguing class of lattices, because they are precisely the lattices obtainable from a closure operator with the so-called anti-exchange property. Moreover, meet-distributive lattices are join semidistributive. Therefore, they admit two natural secondary structures: the core label order is an alternative order on the lattice elements and...
André Sesboüé (1996)
Czechoslovak Mathematical Journal
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Dietmar Schweigert (1985)
Mathematica Slovaca
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Joanna Grygiel (2004)
Discussiones Mathematicae - General Algebra and Applications
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We present a construction of finite distributive lattices with a given skeleton. In the case of an H-irreducible skeleton K the construction provides all finite distributive lattices based on K, in particular the minimal one.
Marcin Łazarz (2019)
Bulletin of the Section of Logic
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Even if a lattice L is not distributive, it is still possible that for particular elements x, y, z ∈ L it holds (x∨y) ∧z = (x∧z) ∨ (y ∧z). If this is the case, we say that the triple (x, y, z) is distributive. In this note we provide some sufficient conditions for the distributivity of a given triple.
Vinayak V. Joshi, B. N. Waphare (2005)
Mathematica Bohemica
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The concept of a 0-distributive poset is introduced. It is shown that a section semicomplemented poset is distributive if and only if it is 0-distributive. It is also proved that every pseudocomplemented poset is 0-distributive. Further, 0-distributive posets are characterized in terms of their ideal lattices.