Uniform Mal’cev algebras with small congruence lattices

A congruence of an algebra is called uniform if all the congruence classes are of the same size. An algebra is called uniform if each of its congruences is uniform. All algebras with a group reduct have this property. We prove that almost every finite uniform Mal’cev algebra with a congruence lattic...

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Bibliographic Details
Published in:Algebra universalis 2014-08, Vol.72 (1), p.57-69
Main Author: Mudrinski, Nebojša
Format: Article
Language:English
Subjects:
Algebra
Mathematics
Mathematics and Statistics
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Summary:A congruence of an algebra is called uniform if all the congruence classes are of the same size. An algebra is called uniform if each of its congruences is uniform. All algebras with a group reduct have this property. We prove that almost every finite uniform Mal’cev algebra with a congruence lattice of height at most two is polynomially equivalent to an expanded group.
ISSN:0002-5240
1420-8911
DOI:10.1007/s00012-014-0288-x