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Abelian group pairs having a trivial coGalois group. (English) Zbl 1174.20016
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 \(G(A\to B)\), associated to a torsion-free cover, to be trivial for an object \(A\to B\) in \(q_2\). Our results generalize those of E. Enochs and J. Rada for Abelian groups.

MSC:
20K30 Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups
20K40 Homological and categorical methods for abelian groups
13C11 Injective and flat modules and ideals in commutative rings
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References:
[1] E. Enochs and O. Jenda: Relative Homological Algebra. Volume 30 of DeGruyter Expositions in Mathematics, Walter de Gruyter Co., Berlin, Germany (2000). · Zbl 0952.13001
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