A version of purity on local abelian groups

Keef, Patrick W.

doi:10.4171/rsmup/63

Keef, Patrick W.

Rendiconti del Seminario Matematico della Università di Padova, Tome 144 (2020), pp. 159-176.

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Résumé

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

Publié le : 2020-12-10

MR Zbl

DOI : 10.4171/rsmup/63

Classification : 20, 00

@article{RSMUP_2020__144__159_0,
     author = {Keef, Patrick W.},
     title = {A version of purity on local abelian groups},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {159--176},
     volume = {144},
     year = {2020},
     doi = {10.4171/rsmup/63},
     mrnumber = {4186453},
     zbl = {1507.20034},
     language = {en},
     url = {http://www.numdam.org/articles/10.4171/rsmup/63/}
}

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Keef, Patrick W. A version of purity on local abelian groups. Rendiconti del Seminario Matematico della Università di Padova, Tome 144 (2020), pp. 159-176. doi : 10.4171/rsmup/63. http://www.numdam.org/articles/10.4171/rsmup/63/

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