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

Finitely generated equational classes

Aichinger E., Mayr P.: Finitely generated equational classes, in: arXiv, Number arXiv:1403.7938, 2014.

BibTeX

@ARTICLE{
title = {Finitely generated equational classes},
type = {Aufsatz / Paper in Online-Archiv (nicht-referiert)},
author = {Aichinger, Erhard and Mayr, Peter},
language = {EN},
abstract = {Classes of algebraic structures that are defined by equational laws are called varieties or equational classes. A variety is finitely generated if it is defined by the laws that hold in some fixed finite algebra. We show that every subvariety of a finitely generated congruence permutable variety is finitely generated; in fact, we prove the more general result that if a finitely generated variety has an edge term, then all its subvarieties are finitely generated as well. This applies in particular to all varieties of groups, loops, quasigroups and their expansions (e.g., modules, rings, Lie algebras,...).},
journal = {arXiv},
number = {arXiv:1403.7938},
month = {3},
year = {2014},
}

Details

Zusammenfassung: Classes of algebraic structures that are defined by equational laws are called varieties or equational classes. A variety is finitely generated if it is defined by the laws that hold in some fixed finite algebra. We show that every subvariety of a finitely generated congruence permutable variety is finitely generated; in fact, we prove the more general result that if a finitely generated variety has an edge term, then all its subvarieties are finitely generated as well. This applies in particular to all varieties of groups, loops, quasigroups and their expansions (e.g., modules, rings, Lie algebras,...).

Journal: arXiv
Nummer: arXiv:1403.7938
Erscheinungsjahr: 2014
Anzahl Seiten: 17
Reichweite: International

Beteiligte

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

Forschungseinheiten der JKU:

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

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