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

 

Every $ m$-permutable variety satisfies the congruence identity $ \alpha\beta_h= \alpha \gamma_h$


Author: Paolo Lipparini
Journal: Proc. Amer. Math. Soc. 136 (2008), 1137-1144
MSC (2000): Primary 08A30, 08B99, 06B20
Published electronically: December 5, 2007
MathSciNet review: 2367087
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Abstract: It is known that congruence lattices of algebras in $ m$-permutable varieties satisfy non-trivial identities; however, the identities discovered so far are rather artificial and seem to have little intrinsic interest.

We show here that every $ m$-permutable variety satisfies the well-known and well-studied congruence identity $ \alpha \beta_h= \alpha \gamma_h$. We also get a new condition equivalent to $ m$-permutability.


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Additional Information

Paolo Lipparini
Affiliation: Dipartimento di Matematica, Viale della Ricerca Scientifica, II Università di Roma (Rot Vergata), I-00133 Rome, Italy
Email: lipparin@axp.mat.uniroma2.it

DOI: http://dx.doi.org/10.1090/S0002-9939-07-09337-9
PII: S 0002-9939(07)09337-9
Keywords: Congruence $m$-permutable varieties, congruence identities.
Received by editor(s): September 2, 2005
Published electronically: December 5, 2007
Additional Notes: The author has received support from MPI and GNSAGA.
Communicated by: Martin Lorenz
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.