PDF

Discussiones Mathematicae General Algebra and Applications 24(1) (2004) 75-94
DOI: https://doi.org/10.7151/dmgaa.1077

DISTRIBUTIVE LATTICES WITH A GIVEN SKELETON

Joanna Grygiel

Institute of Mathematics and Computer Science,
Pedagogical University of Czestochowa
e-mail: j.grygiel@wsp.czest.pl

Abstract

We present a construction of finite distributive lattices with a given skeleton. In the case of an H-irreducible skeleton K the construction provides all finite distributive lattices based on K, in particular the minimal one.

Keywords: distributive lattice, skeleton, gluing, tolerance relation, skeleton torelance, K-atlas, H-irreducibility.

2000 Mathematics Subject Classification: 06D05, 06C05.

References

[1]	H.J. Bandelt, Tolerance relations of lattices, Bull. Austral. Math. Soc. 23 (1981), 367-381.
[2]	G. Bartenschlager, Free bounded distributive lattices generated by finite ordered sets, Ph.D. Thesis, TH Darmstadt 1994.
[3]	J. Chajda and B. Zelinka, Lattices of tolerances, Casopis Pest. Mat. 102 (1977), 10-24.
[4]	G. Czedli, Factor lattices by tolerances, Acta Sci. Math. (Szeged) 44 (1982), 35-42.
[5]	A. Day and Ch. Herrmann, Gluings of modular lattices, Order 5 (1988), 85-101.
[6]	B. Ganter and R. Wille, Formal concept analysis. Mathematical Foundations, Springer-Verlag, Berlin 1999.
[7]	G. Grätzer, General Lattice Theory, Birkhäuser Verlag, Berlin, 1978.
[8]	J. Grygiel, On gluing of lattices, Bull. Sect. Logic 32 no. 1/2 (2003), 27-32.
[9]	M. Hall and R.P. Dilworth, The embedding problem for modular lattices,Ann. of Math. 45 (1944), 450-456.
[10]	Ch. Herrmann, S-verklebte Summen von Verbänden, Math. Z. 130 (1973), 255-274.
[11]	Ch. Herrmann, Alan Day's work on modular and Arguesian lattices, Algebra Universalis 34 (1995), 35-60.
[12]	R. Wille, The skeletons of free distributive lattices, Discrete Math. 88 (1991), 309-320.

Received 25 October 2003
Revised 12 February 2004