Geodesic
A version of purity on local abelian groups
Rendiconti del Seminario Matematico della Università di Padova, Tome 144 (2020), pp. 159-176

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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 ∏ 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 :
DOI : 10.4171/rsmup/63
Classification : 20, 00 
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     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://geodesic.mathdoc.fr/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

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