| 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:
|
http://hdl.handle.net/10338.dmlcz/140440 |
| . |
| 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 |
| . |
