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Congruence Lattices of Finite Semimodular Lattices

Published online by Cambridge University Press:  20 November 2018

G. Grätzer ,
H. Lakser  and
E. T. Schmidt
G. Grätzer
Affiliation:
Department of Mathematics University of Manitoba Winnipeg, Manitoba R3T 2N2, e-mail: [email protected]
H. Lakser
Affiliation:
Department of Mathematics University of Manitoba Winnipeg, Manitoba R3T 2N2, e-mail: [email protected]
E. T. Schmidt
Affiliation:
Mathematical Institute Technical University of Budapest Műegyetem rkp. 3 H-1521 Budapest Hungary, e-mail: [email protected]
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Abstract

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We prove that every finite distributive lattice can be represented as the congruence lattice of a finite (planar) semimodular lattice.

Keywords

06B1008A05Congruence latticesemimodularplanarfinite
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 41 , Issue 3 , 01 September 1998 , pp. 290 - 297
Copyright
Copyright © Canadian Mathematical Society 1998

References

1. Dilworth, R. P., The Dilworth theorems. Selected papers of Robert P. Dilworth (Eds. Kenneth P. Bogart, Ralph Freese and Joseph P. S. Kung). Contemporary Mathematicians. Birkhäuser Boston, Inc., Boston, MA, 1990.Google Scholar
2. Grätzer, G., General Lattice Theory. Pure Appl. Math., Academic Press, New York; Mathematische Reihe, Band 52, Birkhäuser Verlag, Basel; Akademie Verlag, Berlin, 1978.Google Scholar
3. Grätzer, G. and Lakser, H., Homomorphisms of distributive lattices as restrictions of congruences. Canad. J. Math. 38 (1986), 1122–1134.Google Scholar
4. Grätzer, G. and Lakser, H., Congruence lattices of planar lattices. Acta Math. Hungar. 60 (1992), 251–268.Google Scholar
5. Grätzer, G., Lakser, H. and Schmidt, E. T., Congruence lattices of small planar lattices. Proc.Amer.Math. Soc. 123 (1995), 2619–2623.Google Scholar
6. Grätzer, G., Rival, I. and Zaguia, N., Small representations of finite distributive lattices as congruence lattices. Proc. Amer. Math. Soc. 123 (1995), 1959–1961.Google Scholar
7. Grätzer, G. and Schmidt, E. T., On congruence lattices of lattices. ActaMath. Acad. Sci.Hungar. 13 (1962), 179–185.Google Scholar
8. Grätzer, G. and Schmidt, E. T., Congruence-preserving extensions of finite lattices to sectionally complemented lattices. (Submitted to Proc. Amer. Math. Soc.)Google Scholar
9. Grätzer, G. and Schmidt, E. T., Congruence lattices of finite semimodular lattices. Abstracts Amer. Math. Soc. 97T-06-56.Google Scholar