Direct Sums of Self-Small Mixed Groups

Abstract

The class G of self-small mixed abelian groups of finite rank has recently been the focus of a number of investigations. It is known that, up to quasi-isomorphism, G is dual to the category of locally free torsion-free abelian groups of finite rank. We utilize the reduced mixed groups in G as building blocks of a more extensive class ∑G, the smallest class containing the reduced groups in G that is closed under taking infinite direct sums and direct summands. Our central result is the determination of a complete set of isomorphism invariants for the groups in ∑G. We supplement this broad classification theorem with an investigation of the fine structure of completely decomposable groups in ∑G.