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Finite distributive lattices and doubly irreducible elements

โœ Scribed by Joel Berman; Gabriela Bordalo

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
350 KB
Volume
178
Category
Article
ISSN
0012-365X

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โœฆ Synopsis

For a finite ordered set G let ~(G) denote the family of all distributive lattices L such that G both generates L and is the set of doubly irreducible elements of L. We provide a characterization for membership in ~(G), and by means of this characterization define a natural order relation on ~(G). We show that this order is a boolean lattice and we describe the maximal and minimal elements in this lattice. The maximal element is familiar: the free distributive lattice freely generated by the ordered set G.

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