Processing math: 100%

Boolean lattices

Abbreviation: BoolLat

Definition

A \emph{Boolean lattice} is a bounded distributive lattice L=L,,0,,1 such that

every element has a complement: y(xy=1 and xy=0)

Morphisms

Let L and M be bounded distributive lattices. A morphism from L to M is a function h:LM that is a bounded lattice homomorphism:

h(xy)=h(x)h(y), h(xy)=h(x)h(y), h(0)=0, h(1)=1

Examples

Example 1: P(S),,,,S, the collection of subsets of a set S, with union, empty set, intersection, and the whole set S.

Basic results

Properties

Finite members

Any finite member is a power of the 2-element Boolean lattice.

Subclasses

Superclasses

References


QR Code
QR Code boolean_lattices (generated for current page)