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Keywords:
coGalois group; torsion-free covers; pairs of modules
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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[2] Enochs, E., Rada, J.: Abelian groups which have trivial absolute coGalois group. Czech. Math. Jour. 55 433-437 (2005). DOI 10.1007/s10587-005-0033-x | MR 2137149 | Zbl 1081.20064
[3] Wesley, M.: Torsionfree covers of graded and filtered modules. Ph.D. thesis, University of Kentucky (2005). MR 2707058
[4] Dunkum, M.: Torsion free covers for pairs of modules. Submitted.
[5] Wakamatsu, T.: Stable equivalence for self-injective algebras and a generalization of tilting modules. J. Algebra 134 (1990), 298-325. DOI 10.1016/0021-8693(90)90055-S | MR 1074331 | Zbl 0726.16009
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