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Reports on Mathematical Logic

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No. 31

Joanna GRYGIEL, Piotr WOJTYLAK:

The uniqueness of the decomposition of distributive lattices into sums of Boolean lattices
A b s t r a c t.
We prove that any decomposition of any finite distributive lattice into (the
Wro\'nski sum of) Boolean algebras contains all maximal Boolean fragments of
the lattice. The maximal elements of the decomposition are thus uniquely
determined. We also exhibit a practical method of finding them.

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