# zbMATH — the first resource for mathematics

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
##### Keywords:
coGalois groups; torsion-free covers; pairs of modules
Full Text:
##### 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 [2] E. Enochs and J. Rada: Abelian groups which have trivial absolute coGalois group. Czech. Math. Jour. 55 (2005), 433–437. · Zbl 1081.20064 · doi:10.1007/s10587-005-0033-x [3] M. Wesley: Torsionfree covers of graded and filtered modules. Ph.D. thesis, University of Kentucky, 2005. [4] M. Dunkum: Torsion free covers for pairs of modules. Submitted. · Zbl 1224.13015 [5] T. Wakamatsu: Stable equivalence for self-injective algebras and a generalization of tilting modules. J. Algebra 134 (1990), 298–325. · Zbl 0726.16009 · doi:10.1016/0021-8693(90)90055-S
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.