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ArticleOriginal scientific text

Title

Distributive ordered sets and relative pseudocomplements

Authors 1

Affiliations

  1. Masaryk University, Faculty of Science, Department of Algebra and Geometry, Janáčkovo náměstí 2a, 60200 Brno, Czechoslovakia

Abstract

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.

Keywords

ENG
Brouwerian ordered set, distributive ordered set, relative pseudocomplement

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Discussiones Mathematicae - General Algebra and Applications
2006/26/2
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Pages:
163-181
Main language of publication
English
Received
2006-01-02
Accepted
2006-01-31
Published
2006

DOI: 10.7151/dmgaa.1110

Exact and natural sciences