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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2510.09863 |
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| _version_ | 1866912642446131200 |
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| author | Gunduz, Abuzer |
| author_facet | Gunduz, Abuzer |
| contents | Let $R_1$ and $R_2$ be commutative rings with $1\neq 0,\;M$ and $N$ be unitary $R_1-$module and $R_2-$module, respectively. $f:R_1\rightarrow R_2$ be a ring homomorphism and $φ: M\rightarrow N$ be an $R-$module homomorphism. This article studied $2-$absorbing submodule that is a generalization of the concept of prime submodule. Firstly, some characterizations of $2-$absorbing submodule are presented. Then, we examine the notion of $2-$absorbing submodule in amalgamation module $M \bowtie^φ JN$. We detected when $F\bowtie^φJN$ is a $2-$absorbing submodule of $M \bowtie^φ JN$ by using the isomorphism $\frac{M \bowtie^φ JN}{F \bowtie^φ JN} \cong \frac{M}{F}$ and the homomorphism $p_γ: M \bowtie^φ JN \rightarrow φ(M)+JN$, where $J$ be an ideal of $R_2$ and $F$ be a submodule of $M.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_09863 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On 2-absorbing submodules and their Amalgamations Gunduz, Abuzer Commutative Algebra 13C99, 13C13, 16P60 Let $R_1$ and $R_2$ be commutative rings with $1\neq 0,\;M$ and $N$ be unitary $R_1-$module and $R_2-$module, respectively. $f:R_1\rightarrow R_2$ be a ring homomorphism and $φ: M\rightarrow N$ be an $R-$module homomorphism. This article studied $2-$absorbing submodule that is a generalization of the concept of prime submodule. Firstly, some characterizations of $2-$absorbing submodule are presented. Then, we examine the notion of $2-$absorbing submodule in amalgamation module $M \bowtie^φ JN$. We detected when $F\bowtie^φJN$ is a $2-$absorbing submodule of $M \bowtie^φ JN$ by using the isomorphism $\frac{M \bowtie^φ JN}{F \bowtie^φ JN} \cong \frac{M}{F}$ and the homomorphism $p_γ: M \bowtie^φ JN \rightarrow φ(M)+JN$, where $J$ be an ideal of $R_2$ and $F$ be a submodule of $M.$ |
| title | On 2-absorbing submodules and their Amalgamations |
| topic | Commutative Algebra 13C99, 13C13, 16P60 |
| url | https://arxiv.org/abs/2510.09863 |