A projective characterization for SKT-modules
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- by Brian D. Wick PDF
- Proc. Amer. Math. Soc. 80 (1980), 39-43 Request permission
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.References
- R. B. Warfield Jr., A classification theorem for abelian $p$-groups, Trans. Amer. Math. Soc. 210 (1975), 149–168. MR 372071, DOI 10.1090/S0002-9947-1975-0372071-2
- R. B. Warfield Jr., Classification theory of abelian groups. I. Balanced projectives, Trans. Amer. Math. Soc. 222 (1976), 33–63. MR 422455, DOI 10.1090/S0002-9947-1976-0422455-X
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 80 (1980), 39-43
- MSC: Primary 20K25
- DOI: https://doi.org/10.1090/S0002-9939-1980-0574505-4
- MathSciNet review: 574505