Hostname: page-component-7dd5485656-zlgnt Total loading time: 0 Render date: 2025-10-31T16:51:29.180Z Has data issue: false hasContentIssue false
  • English
  • Français

Tolerance relations on lattices

Published online by Cambridge University Press:  17 April 2009

Hans-J. Bandelt
Hans-J. Bandelt
Affiliation:
Universität Oldenburg, Fachbereich IV - Mathematik, Ammerländer Heerstrasse 67–99, Postfach 2503, 2900 Oldenburg, F.R. Germany.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The lattice of all tolerance relations (that is, reflexive, symmetric compatible relations) on a lattice is investigated. For modular lattices some examples are given which show that such relations do naturally occur.

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 23 , Issue 3 , June 1981 , pp. 367 - 381
Copyright
Copyright © Australian Mathematical Society 1981

References

[1]Bandelt, Hans-J., “Local polynomial functions on lattices”, Houston J. Math. (to appear).Google Scholar
[2]Bandelt, Hans-J., “Tolerances on median algebras”, submitted.Google Scholar
[3]Chajda, Ivan, “Notes on lattice congruences”, Časopis Pěst. Mat. 103 (1978), 255–258.Google Scholar
[4]Chajda, Ivan, “A characterization of distributive lattices by tolerance lattices”, Arch. Math. (Brno) 15 (1979), 203–204.Google Scholar
[5]Chajda, Ivan and Zelinka, Bohdan, “Lattices of tolerances”, Časopis Pěst. Mat. 102 (1977), 10–21.CrossRefGoogle Scholar
[6]Chajda, Ivan and Zelinka, Bohdan, “Minimal compatible tolerances on lattices”, Czechoslovak Math. J. 27 (102) (1977), 452–459.CrossRefGoogle Scholar
[7]Chajda, Ivan and Zelinka, Bohdan, “Tolerances and convexity”, Czechoslovak Math. J. 29 (104) (1979), 584–587.CrossRefGoogle Scholar
[8]Fried, E. and Schmidt, E.T., “Standard sublattices”, Algebra Universalis 5 (1975), 203–211.CrossRefGoogle Scholar
[9]Grätzer, George, General lattice theory (Birkhäuser Verlag, Basel and Stuttgart, 1978).CrossRefGoogle Scholar
[10]Herrmann, Christian, “S-verklebte Summen von Verbänden”, Math. Z. 130 (1973), 255–274.CrossRefGoogle Scholar
[11]Jakubík, J., “Conditionally α-complete sublattices of a distributive lattice”, Algebra Universalis 2 (1972), 255–261.CrossRefGoogle Scholar
[12]Kindermann, M., “Über die Äquivalenz von Ordnungspolynomvoll-ständigkeit und Toleranzeinfachheit endlicher Verbände”, Contributions to general algebra, 145–149 (Proc. Klagenfurt Conf., Klagenfurt, 1978. Verlag Johannes Heyn, Klagenfurt, 1979).Google Scholar
[13] Г.Ч. Куринной [Kurinnoĭ, G.Č.], “Новое доказатвльство творемы Дилуорса” [A new proof of a theorem of Dilworth], Vestnik Har'kov. Gos. Univ. No. 93Mat. Vyp. 38 (1973), 11–15, 1.Google Scholar
[14]Mitschke, Aleit und Wille, Rudolf, “Freie modulare Verbände FM(DM3)”,Proceedings of the University of Houston Lattice Theory Conference,Houston, Texas,1973,383–396 (Department of Mathematics, University of Houston, Houston, Texas, 1973).Google Scholar
[15]Varlet, J.C., “A generalization of the notion of pseudo-complementedness”, Bull. Soc. Roy. Sci. Liège 37 (1968), 149–158.Google Scholar