# distributive lattice

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## distributive lattice

(mathematics)
A lattice in which “greatest lower bound” obeys a distributive law with respect to “least upper bound,” and vice versa.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

## distributive lattice

(theory)
A lattice for which the least upper bound (lub) and greatest lower bound (glb) operators distribute over one another so that

a lub (b glb c) == (a lub c) glb (a lub b)

and vice versa.

("lub" and "glb" are written in LateX as \sqcup and \sqcap).
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References in periodicals archive ?
A distributive lattice is a lattice which satisfies the distributive laws [3].
The set of [alpha]-orientations of a plane graph has a natural distributive lattice structure.
The basic concept behind this ordering is distributive lattice with their relations.
If distributive laws hold in a lattice then it is called a distributive lattice.
As a generalization of completely distributive lattice, the following concept of GCD lattices was introduced in [6].
A distributive lattice L is a lattice which satisfies either of the distributive laws and whose addition + and the multiplication ?
Wu: Fuzzy ideals on a distributive lattice, Fuzzy Sets and Systems, 35(1990), 231-240.
In Theorem 1.5, if [W.sup.J] is a distributive lattice, then the length function l also serves as a rank function, so [W.sup.J](q) is the rank-generating function.
L always denotes a completely distributive lattice and if the lattices L does not contain the zero element and unit element I
Corollary 2.14.[5] Every distributive lattice is a modular lattice.
If we order P (seen as a set of sets of worlds) by [contains or equals to], we obtain a complete distributive lattice (P, [contains or equals to]) with the sentence F at the top and the sentence T at the bottom.

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