On the special context of independent sets
Discussiones Mathematicae. General Algebra and Applications, Tome 21 (2001) no. 1, pp. 115-122.

Voir la notice de l'article provenant de la source Library of Science

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.
Keywords: context, complete lattice, join-independent and meet-independent sets
@article{DMGAA_2001_21_1_a10,
     author = {Slez\'ak, Vladim{\'\i}r},
     title = {On the special context of independent sets},
     journal = {Discussiones Mathematicae. General Algebra and Applications},
     pages = {115--122},
     publisher = {mathdoc},
     volume = {21},
     number = {1},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGAA_2001_21_1_a10/}
}
TY  - JOUR
AU  - Slezák, Vladimír
TI  - On the special context of independent sets
JO  - Discussiones Mathematicae. General Algebra and Applications
PY  - 2001
SP  - 115
EP  - 122
VL  - 21
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGAA_2001_21_1_a10/
LA  - en
ID  - DMGAA_2001_21_1_a10
ER  - 
%0 Journal Article
%A Slezák, Vladimír
%T On the special context of independent sets
%J Discussiones Mathematicae. General Algebra and Applications
%D 2001
%P 115-122
%V 21
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGAA_2001_21_1_a10/
%G en
%F DMGAA_2001_21_1_a10
Slezák, Vladimír. On the special context of independent sets. Discussiones Mathematicae. General Algebra and Applications, Tome 21 (2001) no. 1, pp. 115-122. http://geodesic.mathdoc.fr/item/DMGAA_2001_21_1_a10/

[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.