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Duke Mathematical Journal, 1952 A lattice L is infinitely (join) distributive if a ∩ ∪ B b = ∪ B (a ∩ b) whenever the indicated joins exist in L. Clearly infinite distributivity implies ordinary distributivity. On the other hand it is easy to give examples of distributive lattices which are not infinitely distributive. For example, the rational integers under the relation of division
Dilworth, R. P., McLaughlin, J. E.
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Distributive lattices with strong endomorphism kernel property as direct sums [PDF]
Categories and General Algebraic Structures with Applications, 2020 Unbounded distributive lattices which have strong endomorphism kernel property (SEKP) introduced by Blyth and Silva in [3] were fully characterized in [11] using Priestley duality (see Theorem 2.8}). We shall determine the structure of special elements (
Jaroslav Gurican
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Distribution of Lattice Points [PDF]
Computing, 2006 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Principal and syntactic congruences in congruence-distributive and congruence-permutable varieties [PDF]
, 2008 We give a new proof that a finitely generated congruence-distributive variety has finitely determined syntactic congruences (or, equivalently, term finite principal congruences), and show that the same does not hold for finitely generated congruence ...
McKenzie, Ralph +3 more
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On Quasi-P-Almost Distributive Lattices
Discussiones Mathematicae - General Algebra and Applications, 2020 In this paper, the concept of quasi pseudo-complementation on an Almost Distributive Lattice (ADL) as a generalization of pseudo-complementation on an ADL is introduced and its properties are studied.
Bandaru Ravi Kumar, Rao G.C.
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K-FILTERS OF DISTRIBUTIVE LATTICES [PDF]
Journal of Algebraic SystemsThe concept of K-filters is introduced in distributive lattices and studied some properties of these classes of filters. Some necessary and sufficient conditions are derived for every π-filter of a distributive lattice to become a K-filter.
Mukkamala Sambasiva Rao
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Evolution on distributive lattices [PDF]
Journal of Theoretical Biology, 2006 22 pages, 4 figures; minor corrections, moved details to appendix.
Beerenwinkel, Niko +2 more
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Homology of distributive lattices [PDF]
Journal of Homotopy and Related Structures, 2012 We outline the theory of sets with distributive operations: multishelves and multispindles, with examples provided by semi-lattices, lattices and skew lattices. For every such a structure we define multi-term distributive homology and show some of its properties.
Józef Henryk Przytycki +1 more
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Varieties of Distributive Rotational Lattices [PDF]
, 2013 summary:A rotational lattice is a structure $\langle L;\vee ,\wedge , g\rangle $ where $L=\langle L;\vee ,\wedge \rangle $ is a lattice and $g$ is a lattice automorphism of finite order.
Czédli, Gábor, Nagy, Ildikó V.
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Congruences on a Distributive Lattice [PDF]
Proceedings of the Edinburgh Mathematical Society, 1954 Among the many papers on the subject of lattices I have not seen any simple discussion of the congruences on a distributive lattice. It is the purpose of this note to give such a discussion for lattices with a certain finiteness. Any distributive lattice is isomorphic with a ring of sets (G. Birkhoff, Lattice Theory, revised edition, 1948, p.
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