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Let G be an abelian group and ◻ G its square subgroup as defined in the introduction. We show that the square subgroup of a non-homogeneous and indecomposable torsion-free group G of rank two is a pure subgroup of G and that G/◻ G is a nil group.
In this paper we consider completely decomposable torsion-free groups and we determine the subgroups which are ideals in every ring over such groups.
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