# Distributive ordered sets and relative pseudocomplements

Discussiones Mathematicae - General Algebra and Applications (2006)

- Volume: 26, Issue: 2, page 163-181
- ISSN: 1509-9415

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topJosef Niederle. "Distributive ordered sets and relative pseudocomplements." Discussiones Mathematicae - General Algebra and Applications 26.2 (2006): 163-181. <http://eudml.org/doc/276862>.

@article{JosefNiederle2006,

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.},

author = {Josef Niederle},

journal = {Discussiones Mathematicae - General Algebra and Applications},

keywords = {Brouwerian ordered set; distributive ordered set; relative pseudocomplement; characteristic lattice; antiblocking},

language = {eng},

number = {2},

pages = {163-181},

title = {Distributive ordered sets and relative pseudocomplements},

url = {http://eudml.org/doc/276862},

volume = {26},

year = {2006},

}

TY - JOUR

AU - Josef Niederle

TI - Distributive ordered sets and relative pseudocomplements

JO - Discussiones Mathematicae - General Algebra and Applications

PY - 2006

VL - 26

IS - 2

SP - 163

EP - 181

AB - 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.

LA - eng

KW - Brouwerian ordered set; distributive ordered set; relative pseudocomplement; characteristic lattice; antiblocking

UR - http://eudml.org/doc/276862

ER -

## References

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- [8] J. Niederle, Semimodularity and irreducible elements, Acta Sci. Math. (Szeged) 64 (1998), 351-356 Zbl0924.06012
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- [10] J. Niederle, On pseudocomplemented and Stone ordered sets, addendum, Order 20 (2003), 347-349 Zbl1059.06001
- [11] J. Niederle, On infinitely distributive ordered sets, Math. Slovaca 55 (2005), 495-502 Zbl1150.06002
- [12] G. Szász, Einführung in die Verbandstheorie, Akadémiai Kiadó, Budapest 1962.

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