Hokkaido Mathematical Journal

A projective characterization of a class of abelian groups

Patrick W. KEEF

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Abstract

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

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

Dates
First available in Project Euclid: 1 August 2016

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1470080748

Digital Object Identifier
doi:10.14492/hokmj/1470080748

Mathematical Reviews number (MathSciNet)
MR3532122

Zentralblatt MATH identifier
1350.20039

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

Keywords
purity injectives projectives direct sums of cyclics Ulm subgroups

Citation

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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