On localizations of torsion abelian groups

José L. Rodríguez, Jérôme Scherer, and Lutz Strüngmann. "On localizations of torsion abelian groups." Fundamenta Mathematicae 183.2 (2004): 123-138. <http://eudml.org/doc/282959>.

@article{JoséL2004,
abstract = {As is well known, torsion abelian groups are not preserved by localization functors. However, Libman proved that the cardinality of LT is bounded by $|T|^\{ℵ₀\}$ 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.},
author = {José L. Rodríguez, Jérôme Scherer, Lutz Strüngmann},
journal = {Fundamenta Mathematicae},
keywords = {Abelian torsion groups; localization functors; primary components; basic subgroups; categories of Abelian groups},
language = {eng},
number = {2},
pages = {123-138},
title = {On localizations of torsion abelian groups},
url = {http://eudml.org/doc/282959},
volume = {183},
year = {2004},
}

TY - JOUR
AU - José L. Rodríguez
AU - Jérôme Scherer
AU - Lutz Strüngmann
TI - On localizations of torsion abelian groups
JO - Fundamenta Mathematicae
PY - 2004
VL - 183
IS - 2
SP - 123
EP - 138
AB - As is well known, torsion abelian groups are not preserved by localization functors. However, Libman proved that the cardinality of LT is bounded by $|T|^{ℵ₀}$ 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.
LA - eng
KW - Abelian torsion groups; localization functors; primary components; basic subgroups; categories of Abelian groups
UR - http://eudml.org/doc/282959
ER -