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 (2023): 0.6

SJR (2023): 0.214

SNIP (2023): 0.604

Index Copernicus (2022): 121.02

H-Index: 5

Discussiones Mathematicae - General Algebra and Applications

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Discussiones Mathematicae General Algebra and Applications 24(2) (2004) 199-209
DOI: https://doi.org/10.7151/dmgaa.1085

LATTICE-INADMISSIBLE INCIDENCE STRUCTURES

Frantisek Machala and Vladimír Slezák

Department of Algebra and Geometry,
Faculty of Science, Palacký University
Tomkova 40, 779 00 Olomouc, Czech Republic
e-mail: F.Machala@seznam.cz
e-mail: slezakv@seznam.cz

Abstract

Join-independent and meet-independent sets in complete lattices were defined in [6]. According to [6], to each complete lattice(L, Ł ) and a cardinal number p one can assign (in a unique way)an incidence structure J Lp of independent sets of (L, Ł ). In this paper some lattice-inadmissible incidence structures are founded, i.e. such incidence structures that are not isomorphic to any incidence structure JLp.

Keywords: complete lattices, join-independent and meet-independent sets, incidence structures.

Mathematics Subject Classification 2000: 06B23, 08A02, 08A05.

References

[1] P. Crawley and R.P. Dilworth, Algebraic Theory of Lattices, Prentice Hall, Englewood Cliffs 1973.
[2] G. Czédli, A.P. Huhn and E. T. Schmidt, Weakly independent sets in lattices , Algebra Universalis 20 (1985), 194-196.
[3] V. Dlab, Lattice formulation of general algebraic dependence , Czechoslovak Math. J. 20 (95) (1970), 603-615.
[4] B. Ganter and R. Wille, Formale Begriffsanalyse. Mathematische Grundlagen, Springer-Verlag, Berlin 1996; Eglish translation: Formal Concept Analysis. Mathematical Fundations, Springer-Verlag, Berlin 1999.
[5] G. Gratzer, General Lattice Theory, Birkhauser-Verlag, Basel 1998.
[6] F. Machala, Join-independent and meet-independent sets in complete lattices , Order 18 (2001), 269-274.
[7] F. Machala, Incidence structures of independent sets, Acta Univ. Palacki. Olomuc., Fac. Rerum Natur., Math. 38 (1999), 113-118.
[8] F. Machala, Incidence structures of type (p,n), Czechoslovak Math. J. 53 (128) (2003), 9-18.
[9] F. Machala, Special incidence structures of type (p, n), Acta Univ. Palack. Olomuc., Fac. Rerum Natur., Math. 39 (2000), 123-134.
[10] F. Machala, Special incidence structures of type (p, n) - Part II, Acta Univ. Palack. Olomuc., Fac. Rerum Natur., Math. 40 (2001), 131-142.
[11] V. Slezák, On the special context of independent sets, Discuss. Math. - Gen. Algebra Appl. 21 (2001), 115-122.
[12] G. Szász, Introduction to Lattice Theory, Akadémiai Kiadó , Budapest 1963.

Received 21 January 2004
Revised 11 December 2004

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