A version of purity on local abelian groups

Abstract

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 LλG determines the notion of Lλ-purity. Another way of constructing a type of purity, called p w -purity, is defined using the functor Q α<λ(G/p 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, Lλ and p <λ w -purity are compared in a variety of contexts, for example, in the category of Warfield groups. Mathematics Subject Classification (2010). 20K10, 20K40