Any nonmodular lattice contains the lattice (shown below) as a sublattice.
Since is not modular, by definition it contains elements , and such that and . Then the sublattice formed by , , , and is isomorphic to . This is because while by absorption and similarly . Moreover, covers since would imply , whence and contrary to our hypothesis. By the same method, leads to a contradiction of nonmodularity, so covers . ∎
|Date of creation||2013-03-22 16:55:25|
|Last modified on||2013-03-22 16:55:25|
|Last modified by||ixionid (16766)|