Direct products and sums of torsion-free Abelian groups

Let A A be a finite rank, indecomposable torsion-free Abelian group whose p p -ranks are less than two for all primes p p . Let G G be a direct product of copies of A A , and B B be a nonzero countable pure subgroup of G G such that B B is the span of the homomorphic images of A A in B B . Then it is shown that B B is a direct sum of copies of A A . This result is applied to obtain a Krull-Schmidt theorem for direct sums of groups A A from a semirigid class of groups. In particular, if the groups A A have rank one, then the well-known BaerKulikov-Kaplansky theorem is obtained.