Distributive lattices with a given skeleton

Joanna Grygiel

Discussiones Mathematicae - General Algebra and Applications (2004)

  • Volume: 24, Issue: 1, page 75-94
  • ISSN: 1509-9415

Abstract

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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.

How to cite

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Joanna Grygiel. "Distributive lattices with a given skeleton." Discussiones Mathematicae - General Algebra and Applications 24.1 (2004): 75-94. <http://eudml.org/doc/287596>.

@article{JoannaGrygiel2004,
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.},
author = {Joanna Grygiel},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {distributive lattice; skeleton; gluing; tolerance relation; skeleton torelance; K-atlas; H-irreducibility},
language = {eng},
number = {1},
pages = {75-94},
title = {Distributive lattices with a given skeleton},
url = {http://eudml.org/doc/287596},
volume = {24},
year = {2004},
}

TY - JOUR
AU - Joanna Grygiel
TI - Distributive lattices with a given skeleton
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2004
VL - 24
IS - 1
SP - 75
EP - 94
AB - 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.
LA - eng
KW - distributive lattice; skeleton; gluing; tolerance relation; skeleton torelance; K-atlas; H-irreducibility
UR - http://eudml.org/doc/287596
ER -

References

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  1. [1] H.J. Bandelt, Tolerance relations of lattices, Bull. Austral. Math. Soc. 23 (1981), 367-381. Zbl0449.06005
  2. [2] G. Bartenschlager, Free bounded distributive lattices generated by finite ordered sets, Ph.D. Thesis, TH Darmstadt 1994. 
  3. [3] J. Chajda and B. Zelinka, Lattices of tolerances, Casopis Pest. Mat. 102 (1977), 10-24. Zbl0354.08011
  4. [4] G. Czedli, Factor lattices by tolerances, Acta Sci. Math. (Szeged) 44 (1982), 35-42. Zbl0484.06010
  5. [5] A. Day and Ch. Herrmann, Gluings of modular lattices, Order 5 (1988), 85-101. 
  6. [6] B. Ganter and R. Wille, Formal concept analysis. Mathematical Foundations, Springer-Verlag, Berlin 1999. Zbl0909.06001
  7. [7] G. Grätzer, General Lattice Theory, Birkhäuser Verlag, Berlin, 1978. Zbl0436.06001
  8. [8] J. Grygiel, On gluing of lattices, Bull. Sect. Logic 32 no. 1/2 (2003), 27-32. Zbl1059.06004
  9. [9] M. Hall and R.P. Dilworth, The embedding problem for modular lattices, Ann. of Math. 45 (1944), 450-456. Zbl0060.06102
  10. [10] Ch. Herrmann, S-verklebte Summen von Verbänden, Math. Z. 130 (1973), 255-274. 
  11. [11] Ch. Herrmann, Alan Day's work on modular and Arguesian lattices, Algebra Universalis 34 (1995), 35-60. Zbl0838.06002
  12. [12] R. Wille, The skeletons of free distributive lattices, Discrete Math. 88 (1991), 309-320. Zbl0739.06007

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