modular inequality

In any lattice ( the self-dual modular inequalityMathworldPlanetmath is true: if xz then x(yz)(xy)z.


xxy and we are given that xz, so x(xy)z. Also, yzyxy and yzz imply that yz(xy)z. Therefore, x(yz)(xy)z. ∎

Title modular inequality
Canonical name ModularInequality
Date of creation 2014-02-01 1:48:21
Last modified on 2014-02-01 1:48:21
Owner ixionid (16766)
Last modified by ixionid (16766)
Numerical id 10
Author ixionid (16766)
Entry type Theorem
Classification msc 06C05
Related topic ModularLattice
Related topic DistributiveInequalities
Defines modular inequality