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On generation of finite posets by meet-irreducibles. (English) Zbl 0952.06002

Summary: Necessary and sufficient conditions for a finite poset and a finite distributive lattice to have isomorphic posets of meet-irreducible elements are given. Hence, it is proved that every finite partially ordered set with a given poset of meet-irreducibles is order-embeddable into the corresponding finite distributive lattice.

MSC:

06A06 Partial orders, general
06D05 Structure and representation theory of distributive lattices
06B15 Representation theory of lattices
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