If I am proving a lattice is non-distributive i.e. is shown it isomorphic to one of the two lattices in the theorem, is there a quick way to prove it is isomorphic without going through every vertex and showing for every vertex?

Printable View

- November 30th 2010, 06:48 PMdwsmithLattice
If I am proving a lattice is non-distributive i.e. is shown it isomorphic to one of the two lattices in the theorem, is there a quick way to prove it is isomorphic without going through every vertex and showing for every vertex?

- November 30th 2010, 06:50 PMDrexel28
- November 30th 2010, 06:58 PMdwsmith
I have lattice I want to show is isomorphic to another lattice that is always non-distributive so can I prove the lattice is non-distributive. In order to show it is isomorphic, I must show all

glb=greatest lower bound

lub=least upper bound

L is the lattice I want to show is isomorphic to L2 since L2 is always non-distributive.

If I check the glb and lub for ever combination of as and bs, I will have to do this 48 times. Is there a simpler way? - November 30th 2010, 07:04 PMDrexel28
- November 30th 2010, 07:07 PMdwsmith
I have the bijection and what you are saying is the same as the lub and glb are the same.

- November 30th 2010, 07:12 PMDrexel28