Encyclopedia

distributive lattice

Also found in: Wikipedia.

distributive lattice

[di′strib·yəd·iv ′lad·əs]
(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).
This article is provided by FOLDOC - Free Online Dictionary of Computing (foldoc.org)
Mentioned in
References in periodicals archive
A distributive lattice is a lattice which satisfies the distributive laws [3].
On Subdirect Decompositions of Finite Distributive Lattices
The set of [alpha]-orientations of a plane graph has a natural distributive lattice structure.
Mixing times of Markov chains on degree constrained orientations of planar graphs
The basic concept behind this ordering is distributive lattice with their relations.
A mathematical model: preventing active and passive attacks in mobile banking scenario
If distributive laws hold in a lattice then it is called a distributive lattice.
Algebraic structures of neutrosophic soft sets
As a generalization of completely distributive lattice, the following concept of GCD lattices was introduced in [6].
Countably QC-approximating posets
A distributive lattice L is a lattice which satisfies either of the distributive laws and whose addition + and the multiplication ?
On decompositions of matrices over distributive lattices
Wu: Fuzzy ideals on a distributive lattice, Fuzzy Sets and Systems, 35(1990), 231-240.
Generalized ideals with a triangular norm
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.
On orbits of order ideals of minuscule posets
L always denotes a completely distributive lattice and if the lattices L does not contain the zero element and unit element I
A new structure and constructions of L-fuzzy maps
Corollary 2.14.[5] Every distributive lattice is a modular lattice.
The generalized f-derivations of lattices
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.
Comparing theories by their positive and negative contents
Copyright © 2003-2025 Farlex, Inc Disclaimer
All content on this website, including dictionary, thesaurus, literature, geography, and other reference data is for informational purposes only. This information should not be considered complete, up to date, and is not intended to be used in place of a visit, consultation, or advice of a legal, medical, or any other professional.