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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A projective characterization for SKT-modules


Author: Brian D. Wick
Journal: Proc. Amer. Math. Soc. 80 (1980), 39-43
MSC: Primary 20K25
MathSciNet review: 574505
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Abstract: In this paper a class of abelian groups (SKT-modules), which includes the torsion totally projective groups, S-groups, and balanced projectives is shown to be a subclass of a projective class of groups with respect to a naturally defined class of short exact sequences called the ch-projective modules and ch-pure sequences, respectively. Every $ {Z_p}$-module has a ch-pure projective resolution and every reduced ch-projective module is a summand of a SKT-module. It is finally shown that a $ {Z_p}$-module M is ch-projective if and only if, for every ordinal $ \alpha $, the two $ {Z_p}$-modules $ {p^\alpha }M$ and $ M/{p^\alpha }M$ are both ch-projective.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1980-0574505-4
PII: S 0002-9939(1980)0574505-4
Article copyright: © Copyright 1980 American Mathematical Society