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Modularity prevents tails
Author(s):
Keith
A.
Kearnes;
Emil
W.
Kiss
Journal:
Proc. Amer. Math. Soc.
127
(1999),
11-19.
MSC (1991):
Primary 08A05, 08A30, 08B10
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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  have empty tails. The second property is that congruence lattices omit pentagons of type  .
References:
- 1.
- P. Agliano and K. A. Kearnes, Congruence semimodular varieties I: locally finite varieties, Algebra Universalis 32 (1994), 224-269. MR 95i:08010
- 2.
- D. Hobby and R. McKenzie, The Structure of Finite Algebras, Contemporary Mathematics v. 76, American Mathematical Society, 1988. MR 89m:08001
- 3.
- K. A. Kearnes, Type restriction in locally finite varieties with the CEP, Canadian Journal of Mathematics 43 (1991), 748-769. MR 92m:08005
- 4.
- K. A. Kearnes, Cardinality bounds for subdirectly irreducible algebras, Journal of Pure and Applied Algebra 112 (1996), 293-312. MR 97f:08009
- 5.
- K. A. Kearnes, Varieties with a difference term, Journal of Algebra 177 (1995), 926-960. MR 97c:08007
- 6.
- K. A. Kearnes, E. W. Kiss, and M. Valeriote. A geometrical consequence of residual smallness. preprint, 1996.
- 7.
- K. A. Kearnes and R. McKenzie, Residual smallness relativized to congruence types, preprint, 1996.
- 8.
- E. W. Kiss, An easy way to minimal algebras, International Journal of Algebra and Computation 7 (1997), 55-75. MR 98g:08002
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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:
Eötvös University, Department of Algebra and Number Theory, 1088 Budapest, Múzeum krt. 6--8, Hungary -
Email:
ewkiss@cs.elte.hu
DOI:
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
Copyright of article:
Copyright
1999,
American Mathematical Society
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