| Title:
|
On $n$-submodules and $G.n$-submodules (English) |
| Author:
|
Karimzadeh, Somayeh |
| Author:
|
Moghaderi, Javad |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
73 |
| Issue:
|
1 |
| Year:
|
2023 |
| Pages:
|
245-262 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We investigate some properties of $n$-submodules. More precisely, we find a necessary and sufficient condition for every proper submodule of a module to be an $n$-submodule. Also, we show that if $M$ is a finitely generated $R$-module and $ \sqrt {{{\rm Ann} }_R(M)}$ is a prime ideal of $R$, then $M$ has $n$-submodule. Moreover, we define the notion of \hbox {$G.n$-submodule}, which is a generalization of the notion of $n$-submodule. We find some characterizations of $G.n$-submodules and we examine the way the aforementioned notions are related to each other. (English) |
| Keyword:
|
$n$-ideal |
| Keyword:
|
$n$-submodule |
| Keyword:
|
primary submodule |
| MSC:
|
13C13 |
| MSC:
|
16D10 |
| idZBL:
|
Zbl 07655766 |
| idMR:
|
MR4541100 |
| DOI:
|
10.21136/CMJ.2022.0094-22 |
| . |
| Date available:
|
2023-02-03T11:14:20Z |
| Last updated:
|
2025-04-07 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151515 |
| . |
| Reference:
|
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| . |
