This paper first describes a characterization of a lattice L which can be represented as the collection of all up-sets of a poset. It then obtains a representation of a complete distributive lattice L0 which can be embedded into the lattice L such that all infima, suprema, the top and bottom elements are preserved under the embedding by defining a monotonic operator on a poset. This paper finally studies the algebraic characterization of a finite distributive.
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