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

 

Modularity prevents tails


Authors: Keith A. Kearnes and Emil W. Kiss
Journal: Proc. Amer. Math. Soc. 127 (1999), 11-19
MSC (1991): Primary 08A05, 08A30, 08B10
MathSciNet review: 1625765
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Abstract: We establish a direct correspondence between two congruence properties for finite algebras. The first property is that minimal sets of type $\ityp$ have empty tails. The second property is that congruence lattices omit pentagons of type $\ityp$.


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Additional Information

Keith A. Kearnes
Affiliation: Department of Mathematics, University of Louisville, Louisville, Kentucky 40292
Email: kearnes@louisville.edu

Emil W. Kiss
Affiliation: Department of Mathematics, University of Louisville, Louisville, Kentucky 40292; Eötvös University, Department of Algebra and Number Theory, 1088 Budapest, Múzeum krt. 6–8, Hungary
Email: ewkiss@cs.elte.hu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04882-0
PII: S 0002-9939(99)04882-0
Keywords: Tame congruence theory, modular congruence lattice
Received by editor(s): January 8, 1997
Additional Notes: This work was supported by the Hungarian National Foundation for Scientific Research, grant no. 16432, and by the Fields Institute (Toronto, Canada).
Communicated by: Lance W. Small
Article copyright: © Copyright 1999 American Mathematical Society