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arXiv · 2305.10280

Rings whose associated extended zero-divisor graphs are complemented

Driss Bennis·Brahim El Alaoui·Raja L'hamri
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Abstract

Let $R$ be a commutative ring with identity $1\neq 0$. In this paper, we continue the study started in [10] concerning when the extended zero-divisor graph of $R$, $\overline{\Gamma}(R)$, is complemented. We also study when $\overline{\Gamma}(R)$ is uniquely complemented. We give a complete characterization of when $\overline{\Gamma}(R)$ of a finite ring is complemented. Various examples are given using the direct product of rings and idealizations of modules.

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Driss Bennis, Brahim El Alaoui, Raja L'hamri. 2023-05-17. Rings whose associated extended zero-divisor graphs are complemented. https://arxiv.org/abs/2305.10280

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