| Title:
|
Extending modules relative to a torsion theory (English) |
| Author:
|
Doğruöz, Semra |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
58 |
| Issue:
|
2 |
| Year:
|
2008 |
| Pages:
|
381-393 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
An $R$-module $M$ is said to be an extending module if every closed submodule of $M$ is a direct summand. In this paper we introduce and investigate the concept of a type 2 $\tau $-extending module, where $\tau $ is a hereditary torsion theory on $\mathop {\text{Mod}}$-$R$. An $R$-module $M$ is called type 2 $\tau $-extending if every type 2 $\tau $-closed submodule of $M$ is a direct summand of $M$. If $\tau _I$ is the torsion theory on $\mathop {\text{Mod}}$-$R$ corresponding to an idempotent ideal $I$ of $R$ and $M$ is a type 2 $\tau _I$-extending $R$-module, then the question of whether or not $M/MI$ is an extending $R/I$-module is investigated. In particular, for the Goldie torsion theory $\tau _G$ we give an example of a module that is type 2 ${\tau }_G$-extending but not extending. (English) |
| Keyword:
|
torsion theory |
| Keyword:
|
extending module |
| Keyword:
|
closed submodule |
| MSC:
|
16D50 |
| MSC:
|
16D70 |
| MSC:
|
16D90 |
| MSC:
|
16S90 |
| idZBL:
|
Zbl 1166.16014 |
| idMR:
|
MR2411096 |
| . |
| Date available:
|
2009-09-24T11:55:28Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128264 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| . |
