DM-GAA

ISSN 1509-9415 (print version)

ISSN 2084-0373 (electronic version)

https://doi.org/10.7151/dmgaa

Discussiones Mathematicae - General Algebra and Applications

Cite Score: 0.4

SJR: 0.203

SNIP: 0.562

MCQ: 0.12

Index Copernicus: 121.02

Discussiones Mathematicae - General Algebra and Applications

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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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