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Naveen Kumar Kakumanu, Kar Ping Shum (2016)
Discussiones Mathematicae General Algebra and Applications
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In this paper, we prove that the class of P₂-Almost Distributive Lattices and Post Almost Distributive Lattices are equationally definable.
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...
Jerzy Płonka, Werner Poguntke (1976)
Colloquium Mathematicae
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Henri Mühle (2021)
Mathematica Bohemica
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Distributive lattices form an important, well-behaved class of lattices. They are instances of two larger classes of lattices: congruence-uniform and semidistributive lattices. Congruence-uniform lattices allow for a remarkable second order of their elements: the core label order; semidistributive lattices naturally possess an associated flag simplicial complex: the canonical join complex. In this article we present a characterization of finite distributive lattices in terms of the core...
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.
Adam Grabowski (2015)
Formalized Mathematics
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The article continues the formalization of the lattice theory (as structures with two binary operations, not in terms of ordering relations). In the paper, the notion of a pseudocomplement in a lattice is formally introduced in Mizar, and based on this we define the notion of the skeleton and the set of dense elements in a pseudocomplemented lattice, giving the meet-decomposition of arbitrary element of a lattice as the infimum of two elements: one belonging to the skeleton, and the...
Dietmar Schweigert (1985)
Mathematica Slovaca
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David C. Feinstein (1975)
Colloquium Mathematicae
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K. Głazek (1968)
Colloquium Mathematicae
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Maronna, Ricardo (1964)
Portugaliae mathematica
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Hua Mao (2017)
Open Mathematics
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We characterize complete atomistic lattices whose classification lattices are geometric. This implies an proper solution to a problem raised by S. Radeleczki in 2002.
Aleksandr Kravchenko (2007)
Discussiones Mathematicae - General Algebra and Applications
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We consider general properties of lattices of relative colour-families and antivarieties. Several results generalise the corresponding assertions about colour-families of undirected loopless graphs, see [1]. Conditions are indicated under which relative colour-families form a lattice. We prove that such a lattice is distributive. In the class of lattices of antivarieties of relation structures of finite signature, we distinguish the most complicated (universal) objects. Meet decompositions...