Congruence lattices of small planar lattices

Authors:
G. Grätzer, H. Lakser and E. T. Schmidt

Journal:
Proc. Amer. Math. Soc. **123** (1995), 2619-2623

MSC:
Primary 06B10; Secondary 06D05

DOI:
https://doi.org/10.1090/S0002-9939-1995-1301498-5

MathSciNet review:
1301498

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Abstract | References | Similar Articles | Additional Information

Abstract: For a finite distributive lattice *D* with *n* join-irreducible elements, we construct a finite (planar) lattice *L* with elements such that the congruence lattice of *L* is isomorphic to *D*. This improves on an early result of R. P. Dilworth (around 1940) and G. Grätzer and E. T. Schmidt (1962) constructing such a (nonplanar) lattice *L* with elements, and on a recent construction of G. Grätzer and H. Lakser which yields a finite (planar) lattice *L* with elements.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1995-1301498-5

Keywords:
Lattice,
finite,
congruence,
distributive,
planar

Article copyright:
© Copyright 1995
American Mathematical Society