|Title:||Collection of Finite Lattices Generated by a Poset||Journal:||Order: A Journal on the Theory of Ordered Sets and its Applications||Volume:||17||Issue:||2||First page:||129||Last page:||139||Issue Date:||1-Jan-2000||Rank:||M23||ISSN:||0167-8094||DOI:||10.1023/A:1006473619786||Abstract:||
It is proved that the collection of all finite lattices with the same partially ordered set of meet-irreducible elements can be ordered in a natural way so that the obtained poset is a lattice. Necessary and sufficient conditions under which this lattice is Boolean, distributive and modular are given.
|Keywords:||Finite distributive lattice | Finite lattice | Meet-irreducible | Representation of lattices||Publisher:||Springer Link|
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