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Title: Abelian group pairs having a trivial coGalois group (English)
Author: Hill, Paul
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 58
Issue: 4
Year: 2008
Pages: 1069-1081
Summary lang: English
Category: math
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. (English)
Keyword: coGalois group
Keyword: torsion-free covers
Keyword: pairs of modules
MSC: 13C11
MSC: 16D10
MSC: 16G20
MSC: 20K30
MSC: 20K40
idZBL: Zbl 1174.20016
idMR: MR2471166
Date available: 2010-07-21T08:10:24Z
Last updated: 2020-07-03
Stable URL:
Reference: [1] Enochs, E., Jenda, O.: Relative Homological Algebra.Volume 30 of DeGruyter Expositions in Mathematics, Walter de Gruyter Co., Berlin, Germany (2000). Zbl 0952.13001, MR 1753146
Reference: [2] Enochs, E., Rada, J.: Abelian groups which have trivial absolute coGalois group.Czech. Math. Jour. 55 433-437 (2005). Zbl 1081.20064, MR 2137149, 10.1007/s10587-005-0033-x
Reference: [3] Wesley, M.: Torsionfree covers of graded and filtered modules.Ph.D. thesis, University of Kentucky (2005). MR 2707058
Reference: [4] Dunkum, M.: Torsion free covers for pairs of modules.Submitted.
Reference: [5] Wakamatsu, T.: Stable equivalence for self-injective algebras and a generalization of tilting modules.J. Algebra 134 (1990), 298-325. Zbl 0726.16009, MR 1074331, 10.1016/0021-8693(90)90055-S


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