Representation Theorem for Finite Distributive Lattices

Marek Dudzicz

University of Bialystok

Summary.

In the article the representation theorem for finite distributive lattice as rings of sets is presented. Auxiliary concepts are introduced. Namely, the concept of the height of an element, the maximal element in a chain, immediate predecessor of an element and ring of sets. Besides the scheme of induction in finite lattice is proved.

MML Identifier: LATTICE7

Contents (PDF format)

1. Induction in a Finite Lattice
2. Join Irreducible Elements in a Finite Distributive Lattice
3. Representation Theorem

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