Abelian groups of rank greater than 1 are sources of interesting examples. For instance, for every cardinal "d" there exist torsion-free abelian groups of rank "d" that are indecomposable, i.e. cannot be expressed as a direct sum of a pair of their proper subgroups. These examples demonstrate that torsion-free abelian group of rank greater than 1 cannot be simply built by direct sums from torsion-free abelian groups of rank 1, whose theory is well understood. Moreover, for every integer formula_4, there is a torsion-free abelian group of rank formula_5 that is simultaneously a sum of two indecomposable groups, and a sum of "n" indecomposable groups. Hence even the number of indecomposable summands of a group of an even rank greater or equal than 4 is not well-defined.