Direct decompositions of mixed abelian groups

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We consider a sufficiently large subcategory of the category of mixed abelian groups of finite torsion-free rank and its quotient catego ry obtained by annihilating those homomorphisms which factor through the torsion. We prove that the second category provides a good approximation to the first category, but is much simpler: the groups of morphisms in the second category are finite rank torsion-free groups. This renders it possible to exam ine direct decompositions of mixed groups by the same methods as in the case of finite rank torsion-free groups.