The $i$-extended ideal-based cozero-divisor graph of a commutative ring
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866918486777790464 |
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| author | Farshadifar, Faranak |
| author_facet | Farshadifar, Faranak |
| contents | Let R be a commutative ring with identity and let J be an ideal of R. In this paper, we introduce and investigate the notion of the i-extended ideal-based cozero-divisor graph of R. This graph, denoted by $\overline{Γ''}_{Ji}(R)$, is a simple graph of R whose vertex set is ${x \in R \ J : xR + J \not= R}$. Two distinct vertices $x$ and $y$ are adjacent if and only if $x^m \not \in y^nR+J$ and $y^n \not \in x^mR+J$ for some positive integers m and n with $n\leq i$ and $m\leq i$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_05237 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The $i$-extended ideal-based cozero-divisor graph of a commutative ring Farshadifar, Faranak Commutative Algebra Let R be a commutative ring with identity and let J be an ideal of R. In this paper, we introduce and investigate the notion of the i-extended ideal-based cozero-divisor graph of R. This graph, denoted by $\overline{Γ''}_{Ji}(R)$, is a simple graph of R whose vertex set is ${x \in R \ J : xR + J \not= R}$. Two distinct vertices $x$ and $y$ are adjacent if and only if $x^m \not \in y^nR+J$ and $y^n \not \in x^mR+J$ for some positive integers m and n with $n\leq i$ and $m\leq i$. |
| title | The $i$-extended ideal-based cozero-divisor graph of a commutative ring |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2605.05237 |