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coGalois group; torsion-free covers; pairs of modules
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.
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