Uniform Mal'cev algebras with small congruence lattices

Nebojsa Mudrinski

doi:10.1007/s00012-014-0288-x

Uniform Mal'cev algebras with small congruence lattices

Nebojsa Mudrinski

Institute for Algebra

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	57 - 69
Number of pages	13
Journal	Algebra Universalis
Volume	72
Issue number	1
DOIs	https://doi.org/10.1007/s00012-014-0288-x
Publication status	Published - Aug 2014

Fields of science

101 Mathematics
101001 Algebra
101005 Computer algebra
101013 Mathematical logic
102031 Theoretical computer science

JKU Focus areas

Computation in Informatics and Mathematics
Engineering and Natural Sciences (in general)

Access to Document

10.1007/s00012-014-0288-x

Cite this

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abstract = "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.",

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year = "2014",

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AB - 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.

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ER -

Uniform Mal'cev algebras with small congruence lattices

Abstract

Fields of science

JKU Focus areas

Access to Document

Other files and links

Algebraic approaches to the description of Mal'cev clones

Cite this

Uniform Mal'cev algebras with small congruence lattices

Abstract

Fields of science

JKU Focus areas

Access to Document

Other files and links

Projects

Algebraic approaches to the description of Mal'cev clones

Cite this