Hokkaido Mathematical Journal

A projective characterization of a class of abelian groups

Patrick W. KEEF

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This paper considers the class of abelian groups that are extensions of subgroups that are direct sums of cyclic groups by factor groups that are also of this form. This class is shown to be the projectives with respect to a natural collection of short exact sequences, and that the corresponding class of injectives consists of those groups whose first Ulm subgroup is pure-injective. This class of projectives is quite extensive, but satisfactory descriptions are given for the countable groups in the class that are either torsion-free, or else mixed groups of torsion-free rank one. Particular attention is paid to the behavior of the groups in these classes under localization at some prime.

Article information

Hokkaido Math. J., Volume 45, Number 1 (2016), 53-74.

First available in Project Euclid: 1 August 2016

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20K20: Torsion-free groups, infinite rank 20K21: Mixed groups 20K35: Extensions 20K40: Homological and categorical methods

purity injectives projectives direct sums of cyclics Ulm subgroups


KEEF, Patrick W. A projective characterization of a class of abelian groups. Hokkaido Math. J. 45 (2016), no. 1, 53--74. doi:10.14492/hokmj/1470080748. https://projecteuclid.org/euclid.hokmj/1470080748

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