Abelian group pairs having a trivial coGalois group

Paul Hill

Czechoslovak Mathematical Journal (2008)

  • Volume: 58, Issue: 4, page 1069-1081
  • ISSN: 0011-4642

Abstract

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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 = ℤ , we find necessary and sufficient conditions for the coGalois group G ( A ⟶ B ) , associated to a torsion-free cover, to be trivial for an object A ⟶ B in q 2 . Our results generalize those of E. Enochs and J. Rado for abelian groups.

How to cite

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Hill, Paul. "Abelian group pairs having a trivial coGalois group." Czechoslovak Mathematical Journal 58.4 (2008): 1069-1081. <http://eudml.org/doc/37886>.

@article{Hill2008,
abstract = {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.},
author = {Hill, Paul},
journal = {Czechoslovak Mathematical Journal},
keywords = {coGalois group; torsion-free covers; pairs of modules; coGalois groups; torsion-free covers; pairs of modules},
language = {eng},
number = {4},
pages = {1069-1081},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Abelian group pairs having a trivial coGalois group},
url = {http://eudml.org/doc/37886},
volume = {58},
year = {2008},
}

TY - JOUR
AU - Hill, Paul
TI - Abelian group pairs having a trivial coGalois group
JO - Czechoslovak Mathematical Journal
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 58
IS - 4
SP - 1069
EP - 1081
AB - 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.
LA - eng
KW - coGalois group; torsion-free covers; pairs of modules; coGalois groups; torsion-free covers; pairs of modules
UR - http://eudml.org/doc/37886
ER -

References

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  1. Enochs, E., Jenda, O., Relative Homological Algebra, Volume 30 of DeGruyter Expositions in Mathematics, Walter de Gruyter Co., Berlin, Germany (2000). (2000) Zbl0952.13001MR1753146
  2. Enochs, E., Rada, J., 10.1007/s10587-005-0033-x, Czech. Math. Jour. 55 433-437 (2005). (2005) Zbl1081.20064MR2137149DOI10.1007/s10587-005-0033-x
  3. Wesley, M., Torsionfree covers of graded and filtered modules, Ph.D. thesis, University of Kentucky (2005). (2005) MR2707058
  4. Dunkum, M., Torsion free covers for pairs of modules, Submitted. 
  5. Wakamatsu, T., 10.1016/0021-8693(90)90055-S, J. Algebra 134 (1990), 298-325. (1990) Zbl0726.16009MR1074331DOI10.1016/0021-8693(90)90055-S

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