Direct Sums of Self-Small Mixed Groups

The class 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, is dual to the category of locally free torsion-free abelian groups of finite rank. We utilize the reduced mixed groups in as building blocks of a more extensive class ∑ , the smallest class containing the reduced groups in 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 ∑ . We supplement this broad classification theorem with an investigation of the fine structure of completely decomposable groups in ∑ .