The extended zero-divisor graph of the amalgamated duplication of a ring along an ideal
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914857509453824 |
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| author | Alaoui, Brahim El L'hamri, Raja |
| author_facet | Alaoui, Brahim El L'hamri, Raja |
| contents | Let $R$ be a commutative ring and $I$ be an ideal of $R$. The amalgamated duplication of $R$ along $I$ is the subring $R\Join I:=\{(r,r+i)| r\in R, i\in I\}$ of $R\times R$. This paper investigates the extended zero-divisor graph of the amalgamated duplication of $R$ along $I$. The purpose of this work is to study when $\overlineΓ(R\Join I)$ and $Γ(R\Join I)$ coincide, to characterize when $\overlineΓ(R\Join I)$ is complete, and to compute the diameter and the girth of $\overlineΓ(R\Join I)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_03022 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The extended zero-divisor graph of the amalgamated duplication of a ring along an ideal Alaoui, Brahim El L'hamri, Raja Commutative Algebra Combinatorics 13A70, 05C25 Let $R$ be a commutative ring and $I$ be an ideal of $R$. The amalgamated duplication of $R$ along $I$ is the subring $R\Join I:=\{(r,r+i)| r\in R, i\in I\}$ of $R\times R$. This paper investigates the extended zero-divisor graph of the amalgamated duplication of $R$ along $I$. The purpose of this work is to study when $\overlineΓ(R\Join I)$ and $Γ(R\Join I)$ coincide, to characterize when $\overlineΓ(R\Join I)$ is complete, and to compute the diameter and the girth of $\overlineΓ(R\Join I)$. |
| title | The extended zero-divisor graph of the amalgamated duplication of a ring along an ideal |
| topic | Commutative Algebra Combinatorics 13A70, 05C25 |
| url | https://arxiv.org/abs/2407.03022 |