JournalsrsmupVol. 144pp. 159–176

A version of purity on local abelian groups

  • Patrick W. Keef

    Whitman College, Walla Walla, USA
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In [6], generalizations of the standard notion of purity on pp-local abelian groups were defined using functorial methods to create injective resolutions. For example, if λ\lambda is a limit ordinal, then for a group GG the completion functor LλGL_\lambda G determines the notion of LλL_\lambda-purity. Another way of constructing a type of purity, called pw<λp^{ < \lambda}_{\mathrm w}-purity, is defined using the functor α<λ(G/pαG)\prod_{\alpha < \lambda} (G/p^\alpha G). Properties of this second type of purity are studied; for example, it is shown to be hereditary if and only if λ\lambda has countable cofinality. In addition, LλL_\lambda and pw<λp^{< \lambda}_{\mathrm w}-purity are compared in a variety of contexts, for example, in the category of Warfield groups.

Cite this article

Patrick W. Keef, A version of purity on local abelian groups. Rend. Sem. Mat. Univ. Padova 144 (2020), pp. 159–176

DOI 10.4171/RSMUP/63