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Aufsatz / Paper in Online-Archiv (nicht-referiert)

On the number of finite algebraic structures

Aichinger E., Mayr P., McKenzie R.: On the number of finite algebraic structures, in: arXiv, Number arXiv:1103.2265, 2011.

BibTeX

@ARTICLE{
title = {On the number of finite algebraic structures},
type = {Aufsatz / Paper in Online-Archiv (nicht-referiert)},
author = {Aichinger, Erhard and Mayr, Peter and McKenzie, Ralph},
language = {EN},
abstract = {We prove that every clone of operations on a finite set A, if it contains a Malcev operation, is finitely related -- i.e., identical with the clone of all operations respecting R for some finitary relation R over A. It follows that for a fixed finite set A, the set of all such Malcev clones is countable. This completes the solution of a problem that was first formulated in 1980, or earlier: how many Malcev clones can finite sets support? More generally, we prove that every finite algebra with few subpowers has a finitely related clone of term operations. Hence modulo term equivalence and a renaming of the elements, there are only countably many finite algebras with few subpowers, and thus only countably many finite algebras with a Malcev term.},
journal = {arXiv},
number = {arXiv:1103.2265},
month = {5},
year = {2011},
}

Details

Zusammenfassung: We prove that every clone of operations on a finite set A, if it contains a Malcev operation, is finitely related -- i.e., identical with the clone of all operations respecting R for some finitary relation R over A. It follows that for a fixed finite set A, the set of all such Malcev clones is countable. This completes the solution of a problem that was first formulated in 1980, or earlier: how many Malcev clones can finite sets support? More generally, we prove that every finite algebra with few subpowers has a finitely related clone of term operations. Hence modulo term equivalence and a renaming of the elements, there are only countably many finite algebras with few subpowers, and thus only countably many finite algebras with a Malcev term.

Journal: arXiv
Nummer: arXiv:1103.2265
Erscheinungsjahr: 2011
Anzahl Seiten: 14
Reichweite: International

Beteiligte

AutorInnen / HerausgeberInnen: Assoz.Univprof. DI Dr. Erhard Aichinger, Priv.-Doz. DI Dr. Peter Mayr, Prof. Dr. Ralph McKenzie

Forschungseinheiten der JKU:

Wissenschaftszweige: 101 Mathematik | 101001 Algebra | 101005 Computeralgebra | 101013 Mathematische Logik | 102031 Theoretische Informatik

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