Geodesic
On localizations of torsion abelian groups
José L. Rodríguez1 ; Jérôme Scherer2 ; Lutz Strüngmann3
1 Área de Geometría y Topología, CITE III Universidad de Almería E-04120 Almería, Spain
2 Departament de Matemàtiques Universitat Autònoma de Barcelona E-08193 Bellaterra, Spain
3 Department of Mathematics University of Duisburg-Essen 45117 Essen, Germany
Fundamenta Mathematicae, Tome 183 (2004) no. 2, pp. 123-138.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

As is well known, torsion abelian groups are not preserved by localization functors. However, Libman proved that the cardinality of $LT$ is bounded by $|T|^{\aleph_0}$ whenever $T$ is torsion abelian and $L$ is a localization functor. In this paper we study localizations of torsion abelian groups and investigate new examples. In particular we prove that the structure of $LT$ is determined by the structure of the localization of the primary components of $T$ in many cases. Furthermore, we completely characterize the relationship between localizations of abelian $p$-groups and their basic subgroups.
DOI : 10.4064/fm183-2-4
Keywords: known torsion abelian groups preserved localization functors however libman proved cardinality bounded aleph whenever torsion abelian localization functor paper study localizations torsion abelian groups investigate examples particular prove structure determined structure localization primary components many cases furthermore completely characterize relationship between localizations abelian p groups their basic subgroups

José L. Rodríguez 1 ; Jérôme Scherer 2 ; Lutz Strüngmann 3

1 Área de Geometría y Topología, CITE III Universidad de Almería E-04120 Almería, Spain
2 Departament de Matemàtiques Universitat Autònoma de Barcelona E-08193 Bellaterra, Spain
3 Department of Mathematics University of Duisburg-Essen 45117 Essen, Germany 
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José L. Rodríguez; Jérôme Scherer; Lutz Strüngmann. On localizations of torsion abelian groups. Fundamenta Mathematicae, Tome 183 (2004) no. 2, pp. 123-138. doi : 10.4064/fm183-2-4. http://geodesic.mathdoc.fr/articles/10.4064/fm183-2-4/

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