# Article

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Keywords:
coGalois group; torsion-free covers; pairs of modules
Summary:
Torsion-free covers are considered for objects in the category \$q_2.\$ Objects in the category \$q_2\$ are just maps in \$R\$-Mod. For \$R = {\mathbb Z},\$ we find necessary and sufficient conditions for the coGalois group \$G(A \longrightarrow B),\$ associated to a torsion-free cover, to be trivial for an object \$A \longrightarrow B\$ in \$q_2.\$ Our results generalize those of E. Enochs and J. Rado for abelian groups.
References:
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