Abstract
Let C be an Abelian group. An Abelian group A from a class X of Abelian groups is said to be C H-definable in X if, for any group B ∈ X, the isomorphism Hom(C,A) ≅ Hom(C,B) implies that A ≅ B. If every group from X is C H-definable in X, then X is called an C H-class. In this paper, we study conditions under which a class of completely decomposable torsion-free Abelian groups is an C H-class, where C is a vector group.
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Original Russian Text © T.A. Beregovaya, 2009, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2009, No. 11, pp. 20–23.
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Beregovaya, T.A. On definability of completely decomposable torsion-free Abelian groups by certain groups of homomorphisms. Russ Math. 53, 16–19 (2009). https://doi.org/10.3103/S1066369X09110036
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DOI: https://doi.org/10.3103/S1066369X09110036