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Tytuł artykułu

Classification systems and their lattice

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We define and study classification systems in an arbitrary CJ-generated complete lattice L. Introducing a partial order among the classification systems of L, we obtain a complete lattice denoted by Cls(L). By using the elements of the classification systems, another lattice is also constructed: the box lattice B(L) of L. We show that B(L) is an atomistic complete lattice, moreover Cls(L)=Cls(B(L)). If B(L) is a pseudocomplemented lattice, then every classification system of L is independent and Cls(L) is a partition lattice.
Twórcy
  • Institute of Mathematics, University of Miskolc, 3515 Miskolc-Egyetemváros, Hungary
Bibliografia
  • [1] R. Beazer, Pseudocomplemented algebras with Boolean congruence lattices, J. Austral. Math. Soc. 26 (1978), 163-168.
  • [2] B. Ganter and R. Wille, Formal Concept Analysis. Mathematical Foundations, Springer-Verlag, Berlin 1999.
  • [3] S. Radeleczki, Concept lattices and their application in Group Technology (Hungarian), 'Proceedings of International Computer Science Conference: microCAD'98 (Miskolc, 1998)', University of Miskolc 1999, 3-8.
  • [4] S. Radeleczki, Classification systems and the decomposition of a lattice into direct products, Math. Notes (Miskolc) 1 (2000), 145-156.
  • [5] E.T. Schmidt, A Survey on Congruence Lattice Representations, Teubner-texte zur Math., Band 42, Leipzig 1982.
  • [6] M. Stern, Semimodular Lattices. Theory and Applications, Cambridge University Press, Cambridge 1999.
  • [7] R. Wille, Subdirect decomposition of concept lattices, Algebra Universalis 17 (1983), 275-287.
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Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1056
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