Distributive Lattice

up:: Lattice

Given a lattice $(X,\wedge ,\vee )$ it is said to be distributive if its operators distribute according to

$$\begin{array}{rl}a\wedge (b\vee c)& =(a\wedge b)\vee (a\wedge c)\\ a\vee (b\wedge c)& =(a\vee b)\wedge (a\vee c)\end{array}$$

Properties

Every distributive and limited lattice has unique complements. This motivates the definition of a Boolean Algebra.

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References

• Notas para um Curso de Física-Matemática, João Carlos Alves Barata. Cap. 02