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Discussiones
Mathematicae General Algebra and Applications 21(1) (2001) 115-122
DOI: https://doi.org/10.7151/dmgaa.1032
ON THE SPECIAL CONTEXT OF INDEPENDENT SETS
Vladimír Slezák
Department of Algebra and Geometry,
Palacký University, Tomkova 40, 779 00 Olomouc, Czech Republic
e-mail: slezak@prfnw.upol.cz
Abstract
In this paper the context of independent sets JLp 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.
Keywords: context, complete lattice, join-independent and meet-independent sets.
2000 Mathematics Subject Classification: 06B23, 08A02, 08A05.
References
| [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. |
Received 2 August 2000
Revised 3 April 2001
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