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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Small representations of finite distributive lattices as congruence lattices


Authors: George Grätzer, Ivan Rival and Nejib Zaguia
Journal: Proc. Amer. Math. Soc. 123 (1995), 1959-1961
MSC: Primary 06B10; Secondary 06D05
MathSciNet review: 1301499
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Abstract: A recent result of G. Grätzer, H. Lakser, and E. T. Schmidt states that for any distributive lattice D with n join-irreducible elements, there exists a lattice L with $ O({n^2})$ elements, whose congruence lattice ConL is isomorphic to D. We show that this result is best possible.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1301499-7
PII: S 0002-9939(1995)1301499-7
Keywords: Congruence lattice, finite lattice, distributive lattice
Article copyright: © Copyright 1995 American Mathematical Society