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2006 | 26 | 2 | 163-181
Tytuł artykułu

Distributive ordered sets and relative pseudocomplements

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Kategorie tematyczne
Rocznik
Tom
26
Numer
2
Strony
163-181
Opis fizyczny
Daty
wydano
2006
otrzymano
2006-01-02
poprawiono
2006-01-31
Twórcy
  • Masaryk University, Faculty of Science, Department of Algebra and Geometry, Janáčkovo náměstí 2a, 60200 Brno, Czechoslovakia
Bibliografia
  • [1] B.A. Davey and H.A. Priestley, Introduction to Lattices and Order, Cambridge University Press, Cambridge 1990.
  • [2] M. Erné, Distributive laws for concept lattices, Algebra Universalis 30 (1993), 538-580
  • [3] G. Grätzer, General Lattice Theory, Akademie-Verlag, Berlin 1978.
  • [4] R. Halaš, Pseudocomplemented ordered sets, Archivum Math. (Brno) 29 (1993), 153-160
  • [5] J. Larmerová and J. Rachůnek, Translations of distributive and modular ordered sets, Acta Univ. Palack. Olom., Math. 27 (1988), 13-23
  • [6] J. Niederle, Boolean and distributive ordered sets: characterization and representation by sets, Order 12 (1995), 189-210
  • [7] J. Niederle, Identities in ordered sets, Order 15 (1999), 271-278
  • [8] J. Niederle, Semimodularity and irreducible elements, Acta Sci. Math. (Szeged) 64 (1998), 351-356
  • [9] J. Niederle, On pseudocomplemented and Stone ordered sets, Order 18 (2001), 161-170
  • [10] J. Niederle, On pseudocomplemented and Stone ordered sets, addendum, Order 20 (2003), 347-349
  • [11] J. Niederle, On infinitely distributive ordered sets, Math. Slovaca 55 (2005), 495-502
  • [12] G. Szász, Einführung in die Verbandstheorie, Akadémiai Kiadó, Budapest 1962.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1110
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