On $Gr$-$C$-$2^{A}$-secondary submodules
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866908700489285632 |
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| author | Alwardat, Thikrayat Al-Zoubi, Khaldoun Al-Dolat, Mohammed |
| author_facet | Alwardat, Thikrayat Al-Zoubi, Khaldoun Al-Dolat, Mohammed |
| contents | Let $Ω$ be a group with identity $e$, $Γ$ be a $Ω$-graded commutative ring and $\Im$ a graded $Γ$-module. In this article, we introduce the concept of $gr$-$C$-$2^{A}$-secondary submodules and investigate some properties of this new class of graded submodules. A non-zero graded submodule $S$ of $\Im$ is said to be a $gr$-$C$-$2^{A}$-secondary submodule if whenever $r,s \in h(Γ)$, $L$ is a graded submodule of $\Im$, and $rs\,S\subseteq L$, then either $r\,S\subseteq L$ or $s\,S \subseteq L$ or $rs \in Gr(Ann_Γ(S))$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_12433 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On $Gr$-$C$-$2^{A}$-secondary submodules Alwardat, Thikrayat Al-Zoubi, Khaldoun Al-Dolat, Mohammed General Mathematics Let $Ω$ be a group with identity $e$, $Γ$ be a $Ω$-graded commutative ring and $\Im$ a graded $Γ$-module. In this article, we introduce the concept of $gr$-$C$-$2^{A}$-secondary submodules and investigate some properties of this new class of graded submodules. A non-zero graded submodule $S$ of $\Im$ is said to be a $gr$-$C$-$2^{A}$-secondary submodule if whenever $r,s \in h(Γ)$, $L$ is a graded submodule of $\Im$, and $rs\,S\subseteq L$, then either $r\,S\subseteq L$ or $s\,S \subseteq L$ or $rs \in Gr(Ann_Γ(S))$. |
| title | On $Gr$-$C$-$2^{A}$-secondary submodules |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2212.12433 |