Finite distributive lattices are congruence lattices of almost-geometric lattices (Q535114)
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scientific article; zbMATH DE number 5886752
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Finite distributive lattices are congruence lattices of almost-geometric lattices |
scientific article; zbMATH DE number 5886752 |
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Finite distributive lattices are congruence lattices of almost-geometric lattices (English)
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11 May 2011
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It is proven that any finite distributive lattice is isomorphic to the lattice of congruences of some finite semimodular lattice having the additional property that the poset of nonzero join-irreducible elements is the cardinal sum of chains having at most two elements. A brief but useful historical sketch concerning representations of distributive lattices as congruence lattices is given in the final section.
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distributive lattice
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semimodular lattice
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congruence lattice
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representation
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