# 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).

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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