Distributive ordered sets and relative pseudocomplements
Josef Niederle
Discussiones Mathematicae - General Algebra and Applications, Tome 26 (2006), p. 163-181 / Harvested from The Polish Digital Mathematics Library
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Brouwerian ordered sets generalize Brouwerian lattices. The aim of this paper is to characterize (α)-complete Brouwerian ordered sets in a manner similar to that used previously for pseudocomplemented, Stone, Boolean and distributive ordered sets. The sublattice (G(P)) in the Dedekind-Mac~Neille completion (DM(P)) of an ordered set (P) generated by (P) is said to be the characteristic lattice of (P). We can define a stronger notion of Brouwerianicity by demanding that both (P) and (G(P)) be Brouwerian. It turns out that the two concepts are the same for finite ordered sets. Further, the so-called antiblocking property of distributive lattices is generalized to distributive ordered sets.

Publié le : 2006-01-01
EUDML-ID : urn:eudml:doc:276862 
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     journal = {Discussiones Mathematicae - General Algebra and Applications},
     volume = {26},
     year = {2006},
     pages = {163-181},
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Josef Niederle. Distributive ordered sets and relative pseudocomplements. Discussiones Mathematicae - General Algebra and Applications, Tome 26 (2006) pp. 163-181. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1110/

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