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2004 | 24 | 2 | 199-209
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Lattice-inadmissible incidence structures

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EN
Abstrakty
EN
Join-independent and meet-independent sets in complete lattices were defined in [6]. According to [6], to each complete lattice (L,≤) and a cardinal number p one can assign (in a unique way) an incidence structure $J^{p}_{L}$ of independent sets of (L,≤). In this paper some lattice-inadmissible incidence structures are founded, i.e. such incidence structures that are not isomorphic to any incidence structure $J^{p}_{L}$.
Twórcy
  • Department of Algebra and Geometry, Faculty of Science, Palacký University, Tomkova 40, 779 00 Olomouc, Czech Republic
  • Department of Algebra and Geometry, Faculty of Science, Palacký University, Tomkova 40, 779 00 Olomouc, Czech Republic
Bibliografia
  • [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.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1085
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