On the genus of the annhilator graph of a commutative ring
Let \(R\) be a commutative ring and \(Z(R)^*\) be its set of non-zero zero-divisors. The annihilator graph of a commutative ring \(R\) is the simple undirected graph \(\operatorname{AG}(R)\) with vertices \(Z(R)^*\), and two distinct vertices \(x\) and \(y\) are adjacent if and only if \(\operatorna...
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| Дата: | 2018 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2018
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/79 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| Резюме: | Let \(R\) be a commutative ring and \(Z(R)^*\) be its set of non-zero zero-divisors. The annihilator graph of a commutative ring \(R\) is the simple undirected graph \(\operatorname{AG}(R)\) with vertices \(Z(R)^*\), and two distinct vertices \(x\) and \(y\) are adjacent if and only if \(\operatorname{ann}(xy)\neq \operatorname{ann}(x)\cup \operatorname{ann}(y)\). The notion of annihilator graph has been introduced and studied by A. Badawi [7]. In this paper, we determine isomorphism classes of finite commutative rings with identity whose \(\operatorname{AG}(R)\) has genus less or equal to one. |
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