Article
| 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 |
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| Category: | math |
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| 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 |
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| Date available: | 2023-02-03T11:14:20Z |
| Last updated: | 2023-09-13 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151515 |
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