| Title:
|
On $\tau$-extending modules (English) |
| Author:
|
Talebi, Y. |
| Author:
|
Mohammadi, R. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
57 |
| Issue:
|
3 |
| Year:
|
2016 |
| Pages:
|
279-288 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we introduce the concept of $\tau$-extending modules by $\tau$-rational submodules and study some properties of such modules. It is shown that the set of all $\tau$-rational left ideals of $_RR$ is a Gabriel filter. An $R$-module $M$ is called $\tau$-extending if every submodule of $M$ is $\tau$-rational in a direct summand of $M$. It is proved that $M$ is $\tau$-extending if and only if $M = Rej_ME(R/\tau(R))\oplus N$, such that $N$ is a $\tau$-extending submodule of $M$. An example is given to show that the direct sum of $\tau$-extending modules need not be $\tau$-extending. (English) |
| Keyword:
|
torsion theory |
| Keyword:
|
$\tau$-rational submodules |
| Keyword:
|
$\tau$-closed submodules |
| Keyword:
|
$\tau$-extending modules |
| MSC:
|
16D10 |
| MSC:
|
16D80 |
| MSC:
|
16D99 |
| idZBL:
|
Zbl 06674879 |
| idMR:
|
MR3554509 |
| DOI:
|
10.14712/1213-7243.2015.172 |
| . |
| Date available:
|
2016-09-22T15:20:00Z |
| Last updated:
|
2018-10-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145833 |
| . |
| Reference:
|
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