Semi n-submodules of modules over commutative rings
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909780245741568 |
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| author | Khashan, Hani Celikel, Ece Yetkin |
| author_facet | Khashan, Hani Celikel, Ece Yetkin |
| contents | Let $R$ be a commutative ring with identity and $M$ a unitary $R$-module. The purpose of this paper is to introduce the concept of semi-$n$-submodules as an extension of semi $n$-ideals and $n$-submodules. A proper submodule $N$ of $M$ is called a semi $n$-submodule if whenever $r\in R$, $m\in M$ with $r^{2}m\in N$, $r\notin\sqrt{0}$ and $Ann_{R}(m)=0$, then $rm\in N$. Several properties, characterizations of this class of submodules with many supporting examples are presented. Furthermore, semi $n$-submodules of amalgamated modules are investigated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_08397 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Semi n-submodules of modules over commutative rings Khashan, Hani Celikel, Ece Yetkin Commutative Algebra 13A15, 13A99 Let $R$ be a commutative ring with identity and $M$ a unitary $R$-module. The purpose of this paper is to introduce the concept of semi-$n$-submodules as an extension of semi $n$-ideals and $n$-submodules. A proper submodule $N$ of $M$ is called a semi $n$-submodule if whenever $r\in R$, $m\in M$ with $r^{2}m\in N$, $r\notin\sqrt{0}$ and $Ann_{R}(m)=0$, then $rm\in N$. Several properties, characterizations of this class of submodules with many supporting examples are presented. Furthermore, semi $n$-submodules of amalgamated modules are investigated. |
| title | Semi n-submodules of modules over commutative rings |
| topic | Commutative Algebra 13A15, 13A99 |
| url | https://arxiv.org/abs/2509.08397 |