On the special context of independent sets

• Autorzy: Vladimír Slezák
• Języki publikacji: EN

Abstrakty

EN

In this paper the context of independent sets $J^{p}_{L}$ is assigned to the complete lattice (P(M),⊆) of all subsets of a non-empty set M. Some properties of this context, especially the irreducibility and the span, are investigated.

Słowa kluczowe

EN

context; complete lattice; join-independent and meet-independent sets

Kategorie tematyczne

• 08A02: Relational systems, laws of composition
• 06B23: Complete lattices, completions
• 08A05: Structure theory

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2001
• Tom: 21
• Numer: 1
• Strony: 115-122

Daty

wydano

2001

otrzymano

2000-08-02

otrzymano

2001-03-04

Twórcy

autor

Vladimír Slezák

• Department of Algebra and Geometry, Palacký University, Tomkova 40, 779 00 Olomouc, Czech Republic

Bibliografia

• [1] V. Dlab, Lattice formulation of general algebraic dependence, Czechoslovak Math. Journal 20 (1970), 603-615.
• [2] B. Ganter, R. Wille, Formale Begriffsanalyse - Mathematische Grundlagen, Springer-Verlag, Berlin 1996. (English version: 1999).
• [3] K. Głazek, Some old and new problems in the independence theory, Colloq. Math. 42 (1979), 127-189.
• [4] G. Gratzer, General Lattice Theory, Birkhäuser-Verlag, Basel 1998.
• [5] F. Machala, Incidence structures of independent sets, Acta Univ. Palacki Olomuc., Fac. Rerum Natur., Math. 38 (1999), 113-118.
• [6] F. Machala, Join-independent and meet-independent sets in complete lattices, Order (submitted).
• [7] E. Marczewski, Concerning the independence in lattices, Colloq. Math. 10 (1963), 21-23.
• [8] V. Slezák, Span in incidence structures defined on projective spaces, Acta Univ. Palack. Olomuc., Fac. Rerum Natur., Mathematica 39 (2000), 191-202.
• [9] G. Szász, Introduction to Lattice Theory, Akadémiai Kiadó, Budapest 1963.
• [10] G. Szász, Marczewski independence in lattices and semilattices, Colloq. Math. 10 (1963), 15-20.

Identyfikatory

DOI

10.7151/dmgaa.1032