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In , generalizations of the standard notion of purity on -local abelian groups were defined using functorial methods to create injective resolutions. For example, if is a limit ordinal, then for a group the completion functor determines the notion of -purity. Another way of constructing a type of purity, called -purity, is defined using the functor . Properties of this second type of purity are studied; for example, it is shown to be hereditary if and only if has countable cofinality. In addition, and -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. 159–176DOI 10.4171/RSMUP/63