Primary Decomposition for Σ-Groups
Don Brunker, Denis A. Higgs · Canadian Mathematical Bulletin · 1988
Abstract A Σ-group is an abelian group on which is given a collection of infinite sums having properties suggested by those of absolutely convergent series in R or C. It is shown that the usual decomposition of a torsion abelian group into its p-components carries over to the case of Σ-groups when the property of being torsion is replaced by an appropriate uniform version. For a certain class of Σ-groups, it turns out that being torsion is already sufficient for primary decomposition to hold.