Tensor products of torsion free Abelian groups of finite rank. (Q1076812)

The author gives a set of criteria which are necessary and sufficient for a torsion-free abelian group B of finite rank to be a tensor product of s torsion-free abelian groups. The characterization is quite technical involving a fixed embedding of B into a vector space and the geometric concept of a Segre manifold. Applications are given to show that a representation of a torsion-free abelian group of finite rank as a tensor product need not be unique.