| Title:
|
A Generalization of Baer's Lemma (English) |
| Author:
|
Dunkum, Molly |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
59 |
| Issue:
|
1 |
| Year:
|
2009 |
| Pages:
|
241-247 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
There is a classical result known as Baer's Lemma that states that an $R$-module $E$ is injective if it is injective for $R$. This means that if a map from a submodule of $R$, that is, from a left ideal $L$ of $R$ to $E$ can always be extended to $R$, then a map to $E$ from a submodule $A$ of any $R$-module $B$ can be extended to $B$; in other words, $E$ is injective. In this paper, we generalize this result to the category $q_{\omega }$ consisting of the representations of an infinite line quiver. This generalization of Baer's Lemma is useful in proving that torsion free covers exist for $q_{\omega }$. (English) |
| Keyword:
|
Baer's Lemma |
| Keyword:
|
injective |
| Keyword:
|
representations of quivers |
| Keyword:
|
torsion free covers |
| MSC:
|
13D30 |
| MSC:
|
16G20 |
| MSC:
|
18G05 |
| idZBL:
|
Zbl 1224.13015 |
| idMR:
|
MR2486628 |
| . |
| Date available:
|
2010-07-20T15:03:23Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140476 |
| . |
| Reference:
|
[1] Baer, R.: Abelian groups that are direct summands of every containing abelian group.Bull. Amer. Math. Soc. 46 800-806 (1940). Zbl 0024.14902, MR 0002886, 10.1090/S0002-9904-1940-07306-9 |
| Reference:
|
[2] Enochs, E.: Torsion free covering modules.Proc. Amer. Math. Soc. 14 884-889 (1963). Zbl 0116.26003, MR 0168617, 10.1090/S0002-9939-1963-0168617-7 |
| Reference:
|
[3] Wesley, M. Dunkum: Torsion free covers of graded and filtered modules.Ph.D. thesis, University of Kentucky (2005). MR 2707058 |
| . |
