Noetherian Rings Whose Annihilating-Ideal Graphs Have finite Genus
| Autor: | Aliniaeifard, Farid, Behboodi, Mahmood, Li, Yuanlin |
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| Rok vydání: | 2015 |
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| Druh dokumentu: | Working Paper |
| Popis: | Let $R$ be a commutative ring and ${\Bbb{A}}(R)$ be the set of ideals with non-zero annihilators. The annihilating-ideal graph of $R$ is defined as the graph ${\Bbb{AG}}(R)$ with vertex set ${\Bbb{A}}(R)^*={\Bbb{A}}\setminus\{(0)\}$ such that two distinct vertices $I$ and $J$ are adjacent if and only if $IJ=(0)$. We characterize commutative Noetherian rings $R$ whose annihilating-ideal graphs have finite genus $\gamma(\Bbb{AG}(R))$. It is shown that if $R$ is a Noetherian ring such that $0<\gamma(\Bbb{AG}(R))<\infty$, then $R$ has only finitely many ideals. Comment: 9 pages, 3 figures. arXiv admin note: text overlap with arXiv:1102.4835 |
| Databáze: | arXiv |
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