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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Quasi-pure projective and injective torsion groups


Authors: W. P. Berlinghoff and J. D. Reid
Journal: Proc. Amer. Math. Soc. 65 (1977), 189-193
MSC: Primary 20K10
DOI: https://doi.org/10.1090/S0002-9939-1977-0470104-3
MathSciNet review: 0470104
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Abstract: This paper characterizes quasi-pure projective (q.p.p.) and quasi-pure injective (q.p.i.) p-groups, and hence characterizes all such (abelian) torsion groups. A p-group is q.p.i. if and only if it is the direct sum of a divisible group and a torsion complete group. A nonreduced p-group is q.p.p. if and only if it is the direct sum of a divisible group and a bounded group; a reduced p-group is q.p.p. if and only if it is a direct sum of cyclic groups.


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DOI: https://doi.org/10.1090/S0002-9939-1977-0470104-3
Keywords: Abelian group, pure exact sequence, quasi-projective, quasi-injective, torsion complete, direct sum of cyclic groups
Article copyright: © Copyright 1977 American Mathematical Society