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Lattice (order)

A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra. It consists of a partially ordered set in which every pair of elements has a unique supremum (also called a least upper bound or join) and a unique infimum (also called a greatest lower bound or meet). An example is given by the power set…

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Overview

Definition

Bounded lattice

Connection to other algebraic structures

Examples

Morphisms of lattices

Properties of lattices

Free lattices

Important lattice-theoretic notions

Applications that use lattice theory

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Lattice (order)

Nodes138
Edges137
Triples5
Avg. degree1.99
Density0.014493
Components1

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Important terminology

lattice displaystyle lattices join set meet element algebraic vee elements also ordered wedge called bounded every leq operations two theory

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
framesinstance ofFor an overview of stronger notions of distributivity that are appropriate for complete lattices and that are used to define more special classes of lattices0.80text
completely distributive latticesinstance ofFor an overview of stronger notions of distributivity that are appropriate for complete lattices and that are used to define more special classes of lattices0.80text
see distributivity in order theory.ModularityFor some applications the distributivity condition is too stronginstance ofFor an overview of stronger notions of distributivity that are appropriate for complete lattices and that are used to define more special classes of lattices0.80text
and the following weaker property is often usefulinstance ofFor an overview of stronger notions of distributivity that are appropriate for complete lattices and that are used to define more special classes of lattices0.80text
see distributivity in order theoryinstance ofFor an overview of stronger notions of distributivity that are appropriate for complete lattices and that are used to define more special classes of lattices0.80text

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