distributive lattice


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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.

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).
References in periodicals archive ?
L always denotes a completely distributive lattice and if the lattices L does not contain the zero element and unit element I
M), [intersection],[union],[phi],M }is a complete distributive lattice and it's represented by following Hass diagram
We generalize the classical map concept into the L- fuzzy map which combines all elements in the domain with elements in the co domain giving correlation degrees which takes its values from a complete distributive lattice in a way that forgets the elements whose membership degrees equal to lattice's zero in the domain and co domain.
Wu: Fuzzy ideals on a distributive lattice, Fuzzy Sets and Systems, 35(1990), 231-240.
Finally, in Section 5 we make some remarks about a new partial order on TSSCPPs obtained via boolean triangles, which reduces in the permutation case to the distributive lattice which is the product of chains of lengths 2, 3, .
In [10], we examined a poset structure on TSSCPPs, which turned out to be a distributive lattice with poset of join irreducibles very similar to that of the ASM lattice.
5] Every distributive lattice is a modular lattice.
Let L be a distributive lattice and D be a generalized f- derivation on L where f : L [right arrow] L is a join-homomorphism.
l) if and only if S is a subdirect product of distributive lattice and a member in [?
Let S be a bi-semilattice, if S satisfies the additional identity x + xy [approximately equal to] x and x + yz [approximately equal to] (x + y)(x + z), then S is said to be a distributive lattice.
Farley and Schmidt answer a similar question for distributive lattices in [6].
Schmidt, Posets that locally resemble distributive lattices, J.