Distributive lattices with a given skeleton
Joanna Grygiel
Discussiones Mathematicae - General Algebra and Applications, Tome 24 (2004), p. 75-94 / Harvested from The Polish Digital Mathematics Library

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.

Publié le : 2004-01-01
EUDML-ID : urn:eudml:doc:287596
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1077,
     author = {Joanna Grygiel},
     title = {Distributive lattices with a given skeleton},
     journal = {Discussiones Mathematicae - General Algebra and Applications},
     volume = {24},
     year = {2004},
     pages = {75-94},
     zbl = {1063.06005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1077}
}
Joanna Grygiel. Distributive lattices with a given skeleton. Discussiones Mathematicae - General Algebra and Applications, Tome 24 (2004) pp. 75-94. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1077/

[000] [1] H.J. Bandelt, Tolerance relations of lattices, Bull. Austral. Math. Soc. 23 (1981), 367-381. | Zbl 0449.06005

[001] [2] G. Bartenschlager, Free bounded distributive lattices generated by finite ordered sets, Ph.D. Thesis, TH Darmstadt 1994.

[002] [3] J. Chajda and B. Zelinka, Lattices of tolerances, Casopis Pest. Mat. 102 (1977), 10-24. | Zbl 0354.08011

[003] [4] G. Czedli, Factor lattices by tolerances, Acta Sci. Math. (Szeged) 44 (1982), 35-42. | Zbl 0484.06010

[004] [5] A. Day and Ch. Herrmann, Gluings of modular lattices, Order 5 (1988), 85-101.

[005] [6] B. Ganter and R. Wille, Formal concept analysis. Mathematical Foundations, Springer-Verlag, Berlin 1999. | Zbl 0909.06001

[006] [7] G. Grätzer, General Lattice Theory, Birkhäuser Verlag, Berlin, 1978. | Zbl 0436.06001

[007] [8] J. Grygiel, On gluing of lattices, Bull. Sect. Logic 32 no. 1/2 (2003), 27-32. | Zbl 1059.06004

[008] [9] M. Hall and R.P. Dilworth, The embedding problem for modular lattices, Ann. of Math. 45 (1944), 450-456. | Zbl 0060.06102

[009] [10] Ch. Herrmann, S-verklebte Summen von Verbänden, Math. Z. 130 (1973), 255-274.

[010] [11] Ch. Herrmann, Alan Day's work on modular and Arguesian lattices, Algebra Universalis 34 (1995), 35-60. | Zbl 0838.06002

[011] [12] R. Wille, The skeletons of free distributive lattices, Discrete Math. 88 (1991), 309-320. | Zbl 0739.06007