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Aufsatz / Paper in SCI-Expanded-Zeitschrift

Finitely generated equational classes

Aichinger E., Mayr P.: Finitely generated equational classes, in: Journal of Pure and Applied Algebra, Volume 220, Page(s) 2816-2827, 2016.

BibTeX

@ARTICLE{
title = {Finitely generated equational classes},
type = {Aufsatz / Paper in SCI-Expanded-Zeitschrift},
author = {Aichinger, Erhard and Mayr, Peter},
language = {EN},
abstract = {Classes of algebraic structures that are defined by equational laws are called \emph{varieties} or \emph{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, \dots).},
pages = {2816-2827},
journal = {Journal of Pure and Applied Algebra},
volume = {220},
issn = {0022-4049},
year = {2016},
url = {http://arxiv.org/abs/1403.7938},
}

Details

Zusammenfassung: Classes of algebraic structures that are defined by equational laws are called \emph{varieties} or \emph{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, \dots).

Journal: Journal of Pure and Applied Algebra
Volume: 220
Erscheinungsjahr: 2016
Seitenreferenz: 2816-2827
Anzahl Seiten: 12
Web: http://arxiv.org/abs/1403.7938 (Preliminary version on arxiv)
ISSN: 0022-4049
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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