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Theorem  :-  A lattice L is not a distributive lattice if and only if L has a sublattice which is isomorphic L1(kite structure) or L2(Pantagon structure).

Anyone, please provide an example. I am not able to understand the theorem.

asked in Set Theory & Algebra by Active (2.4k points)
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Theorem  :-  A lattice L is not a distributive lattice if and only if L has a sublattice which is isomorphic Kite structure Lattice or pantagon Structure Lattice

Kite lattice and Pantagon lattice:

These two are not satisfying distributive property i.e. $x ∧ (y ∨ z) = (x ∧ y) ∨ (x ∧ z)$

So Graph contain these two also not distributive.

answered by Veteran (55.5k points)


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