Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-28T12:37:35.856Z Has data issue: false hasContentIssue false
  • English
  • Français

Central relations on lattices

Part of: Lattices

Published online by Cambridge University Press:  09 April 2009

Dietmar Schweigert
Dietmar Schweigert
Affiliation:
FB MatematikUniversität KaiserslauternD 6750 Kaiserslautern, West 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.

A maximal tolerance of a lattice L without infinite chains is either a congruence or a central relation. A finite lattice L is order-polynomially complete if and only if L is simple and has no central relation.

MSC classification

Secondary: 06B10: Ideals, congruence relations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 35 , Issue 3 , December 1983 , pp. 369 - 372
Copyright
Copyright © Australian Mathematical Society 1983

References

[1]Bandelt, H., ‘Tolerance relations on lattices’, Bull. Austral. Math. Soc. 23 (1981), 367–381.Google Scholar
[2]Birkhoff, G., Lattice theory, 3rd ed. (Amer. Math. Soc. Colloq. Publ., 25, Providence, R.I., 1967).Google Scholar
[3]Chajda, I., ‘Recent results and trends in tolerance on algebras and varieties’, Colloquia Mathematica Societatis János Bolyai 28 Szeged (1979), 69–95.Google Scholar
[4]Hashimoto, J., ‘Congruence relations and congruence classes in lattices’, Osaka J. Math. 15 (1963), 71–86.Google Scholar
[5]Grätzer, G., Universal algebra (New York, 1979).Google Scholar
[6]Grätzer, G. and Schmidt, E. T., ‘On congruence lattices of lattices’, Acta Math. Acad. Sci. Hungar. 13 (1962), 178–185.CrossRefGoogle Scholar
[7]Kindermann, M., ‘Uber die Äquivalenz von Ordnungspolynomivollständigkeit und Toleranzeinfachheit endlicher Verbände’, Contribution to general algebra, Kautschitsch, H. et al. , pp. 145–149 (Klagenfurt, 1979).Google Scholar
[8]Rosenberg, I. G., ‘Uber die funktionale Vollständigkeit in den mehrwertigen Logiken’, Rozpravy Československe Akad. Věd. Řada Mat. Přirod Věd. 80 4 (1970), 1–93.Google Scholar
[9]Schweigert, D., ‘Uber endliche, ordnungspolynomvollständige Verbände’, Monatsh. Math. 78 (1974), 68–76.CrossRefGoogle Scholar
[10]Schweigert, D., ‘Compatible relations of modular and orthomodular lattices’, Proc. Amer. Math. Soc. 81 (1981), 462–463.CrossRefGoogle Scholar
[11]Szymańska, M., ‘On central relations of complete lattices’, Preprint, Warszawa (1981).Google Scholar
[12]Wille, R., ‘Eine Charakterisierung endlicher, ordnungspolynomvollständiger Verbände’, Arch. Math. 28 (1977), 577–560.CrossRefGoogle Scholar