Displaying similar documents to “A Generalization of Baer's Splitting problem on Abelian groups.”

On localizations of torsion abelian groups

José L. Rodríguez, Jérôme Scherer, Lutz Strüngmann (2004)

Fundamenta Mathematicae

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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 | ℵ 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...

Directoid groups

Barry J. Gardner, Michael M. Parmenter (2008)

Czechoslovak Mathematical Journal

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We continue the study of directoid groups, directed abelian groups equipped with an extra binary operation which assigns an upper bound to each ordered pair subject to some natural restrictions. The class of all such structures can to some extent be viewed as an equationally defined substitute for the class of (2-torsion-free) directed abelian groups. We explore the relationship between the two associated categories, and some aspects of ideals of directoid groups.