The zero-divisor graph of an amalgamated algebra
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| author | Azimi, Y. Doustimehr, M. R. |
| author_facet | Azimi, Y. Doustimehr, M. R. |
| contents | Let $R$ and $S$ be commutative rings with identity, $f:R\to S$ a ring homomorphism and $J$ an ideal of $S$. Then the subring $R\bowtie^fJ:=\{(r,f(r)+j)\mid r\in R$ and $j\in J\}$ of $R\times S$ is called the amalgamation of $R$ with $S$ along $J$ with respect to $f$.
In this paper, we generalize and improve recent results on the computation of the diameter of the zero-divisor graph of amalgamated algebras and obtain new results. In particular, we provide new characterizations for completeness of the zero-divisor graph of amalgamated algebra, as well as, a complete description for the diameter of the zero-divisor graph of amalgamations in the special case of finite rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_13457 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The zero-divisor graph of an amalgamated algebra Azimi, Y. Doustimehr, M. R. Commutative Algebra Let $R$ and $S$ be commutative rings with identity, $f:R\to S$ a ring homomorphism and $J$ an ideal of $S$. Then the subring $R\bowtie^fJ:=\{(r,f(r)+j)\mid r\in R$ and $j\in J\}$ of $R\times S$ is called the amalgamation of $R$ with $S$ along $J$ with respect to $f$. In this paper, we generalize and improve recent results on the computation of the diameter of the zero-divisor graph of amalgamated algebras and obtain new results. In particular, we provide new characterizations for completeness of the zero-divisor graph of amalgamated algebra, as well as, a complete description for the diameter of the zero-divisor graph of amalgamations in the special case of finite rings. |
| title | The zero-divisor graph of an amalgamated algebra |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2411.13457 |