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

 

Computing congruence lattices
of finite lattices


Author: Ralph Freese
Journal: Proc. Amer. Math. Soc. 125 (1997), 3457-3463
MSC (1991): Primary 06B10, 06B05, 06B15
MathSciNet review: 1451802
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Abstract: An inequality between the number of coverings in the ordered set $\operatorname{J}({\mathbf{Con\;J}})$ of join irreducible congruences on a lattice $\operatorname{L}$ and the size of ${\mathbf{L}}$ is given. Using this inequality it is shown that this ordered set can be computed in time $O(n^2 \log _2 n)$, where $n=|L|$.


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Additional Information

Ralph Freese
Affiliation: Department of Mathematics, University of Hawaii, Honolulu, Hawaii 96822
Email: ralph@math.hawaii.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-97-04332-3
PII: S 0002-9939(97)04332-3
Keywords: Congruence lattice, algorithm
Received by editor(s): June 11, 1996
Additional Notes: This research was partially supported by NSF grant no. DMS–9500752
Communicated by: Lance W. Small
Article copyright: © Copyright 1997 American Mathematical Society